[ { "id": "https://authors.library.caltech.edu/records/x9vjf-8fj59", "eprint_id": 116086, "eprint_status": "archive", "datestamp": "2023-08-20 08:03:55", "lastmod": "2023-10-23 15:21:28", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sabag-Oron", "name": { "family": "Sabag", "given": "Oron" }, "orcid": "0000-0002-7907-1463" }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Hassibi-B", "name": { "family": "Hassibi", "given": "Babak" } } ] }, "title": "Feedback Capacity of Gaussian Channels with Memory", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2022 IEEE.", "abstract": "We consider the feedback capacity of a MIMO channel whose channel output is given by a linear state-space model driven by the channel inputs and a Gaussian process. The generality of our state-space model subsumes all previous studied models such as additive channels with colored Gaussian noise, and channels with an arbitrary dependence on previous channel inputs or outputs. The main result is a computable feedback capacity expression that is given as a convex optimization problem subject to a detectability condition. We demonstrate the capacity result on the auto-regressive Gaussian noise channel, where we show that even a single time-instance delay in the feedback reduces the feedback capacity significantly in the stationary regime. On the other hand, for large regression parameters, the feedback capacity can be achieved with delayed feedback. Finally, we show that the detectability condition is satisfied for scalar models and conjecture that it is true for MIMO models.", "date": "2022-06-26", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "2547-2552", "id_number": "CaltechAUTHORS:20220804-765679000", "isbn": "978-1-6654-2159-1", "book_title": "2022 IEEE International Symposium on Information Theory (ISIT)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220804-765679000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1109/isit50566.2022.9834799", "resource_type": "book_section", "pub_year": "2022", "author_list": "Sabag, Oron; Kostina, Victoria; et el." }, { "id": "https://authors.library.caltech.edu/records/3vd9p-6t398", "eprint_id": 116090, "eprint_status": "archive", "datestamp": "2023-08-20 08:04:27", "lastmod": "2023-10-23 15:21:35", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Guo-Nian", "name": { "family": "Guo", "given": "Nian" }, "orcid": "0000-0003-4490-328X" }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" } ] }, "title": "Reliability function for streaming over a DMC with feedback", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Channels with feedback, reliability function, joint source-channel coding, variable-length codes, streaming, causal coding, posterior matching", "note": "\u00a9 2022 IEEE. \n\nThis work was supported in part by the National Science Foundation (NSF) under grants CCF-1751356 and CCF-1956386.", "abstract": "Conventionally, posterior matching is investigated in channel coding and block encoding contexts \u2013 the source symbols are equiprobably distributed and are entirely known by the encoder before the transmission. In this paper, we consider a streaming source, whose symbols progressively arrive at the encoder at a sequence of deterministic times. We derive the joint source-channel coding (JSCC) reliability function for streaming over a discrete memoryless channel (DMC) with feedback under regularity conditions. We propose a novel instantaneous encoding phase that operates during the symbol arriving period and that achieves the JSCC reliability function for streaming when followed by a block encoding scheme that achieves the JSCC reliability function for a classical source whose symbols are fully accessible before the transmission. The instantaneous encoding phase partitions the evolving message alphabet into groups whose priors are close to the capacity-achieving distribution, and randomizes the group indices to ensure that the transmitted group index has the capacity-achieving distribution. Surprisingly, the JSCC reliability function for streaming is equal to that for a fully accessible source, implying that the knowledge of the entire symbol sequence before the transmission offers no advantage in terms of the reliability function.", "date": "2022-06-26", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "3204-3209", "id_number": "CaltechAUTHORS:20220804-765703000", "isbn": "978-1-6654-2159-1", "book_title": "2022 IEEE International Symposium on Information Theory (ISIT)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220804-765703000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1751356" }, { "agency": "NSF", "grant_number": "CCF-1956386" } ] }, "doi": "10.1109/isit50566.2022.9834852", "resource_type": "book_section", "pub_year": "2022", "author_list": "Guo, Nian and Kostina, Victoria" }, { "id": "https://authors.library.caltech.edu/records/w8jq1-9y684", "eprint_id": 116087, "eprint_status": "archive", "datestamp": "2023-08-20 08:04:04", "lastmod": "2023-10-23 15:21:38", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Yavas-Recep-Can", "name": { "family": "Yavas", "given": "Recep Can" }, "orcid": "0000-0002-5640-515X" }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Effros-M", "name": { "family": "Effros", "given": "Michelle" }, "orcid": "0000-0003-3757-0675" } ] }, "title": "Third-order Analysis of Channel Coding in the Moderate Deviations Regime", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2022 IEEE. \n\nThis work was supported in part by the National Science Foundation (NSF) under grant CCF-1817241 and CCF-1956386.\n\n
Submitted - 2203.01418.pdf
", "abstract": "The channel coding problem in the moderate deviations regime is studied; here, the error probability sub-exponentially decays to zero, and the rate approaches the capacity slower than O(1/\u221an). The main result refines Altu\u011f and Wagner's moderate deviations result by deriving lower and upper bounds on the third-order term in the asymptotic expansion of the maximum achievable message set size. The third-order term of the expansion employs a new quantity called the channel skewness. For the binary symmetric channel and most practically important (n,\u03f5) pairs, including n \u2208 [100, 500] and \u03f5 \u2208 [10\u207b\u00b9\u2070,10\u207b\u00b9], an approximation up to the channel skewness is the most accurate among several expansions in the literature.", "date": "2022-06-26", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "2309-2314", "id_number": "CaltechAUTHORS:20220804-765685000", "isbn": "978-1-6654-2159-1", "book_title": "2022 IEEE International Symposium on Information Theory (ISIT)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220804-765685000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1817241" }, { "agency": "NSF", "grant_number": "CCF-1956386" } ] }, "doi": "10.1109/isit50566.2022.9834841", "primary_object": { "basename": "2203.01418.pdf", "url": "https://authors.library.caltech.edu/records/w8jq1-9y684/files/2203.01418.pdf" }, "resource_type": "book_section", "pub_year": "2022", "author_list": "Yavas, Recep Can; Kostina, Victoria; et el." }, { "id": "https://authors.library.caltech.edu/records/k6r2v-tvn68", "eprint_id": 116088, "eprint_status": "archive", "datestamp": "2023-08-20 08:04:13", "lastmod": "2023-10-23 15:21:30", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Yang-Hengjie", "name": { "family": "Yang", "given": "Hengjie" }, "orcid": "0000-0003-3356-3726" }, { "id": "Yavas-Recep-Can", "name": { "family": "Yavas", "given": "Recep Can" }, "orcid": "0000-0002-5640-515X" }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Wesel-Richard-D", "name": { "family": "Wesel", "given": "Richard D." }, "orcid": "0000-0002-9139-8098" } ] }, "title": "Variable-Length Stop-Feedback Codes With Finite Optimal Decoding Times for BI-AWGN Channels", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2022 IEEE. \n\nThis research is supported by National Science Foundation (NSF) grant CCF-1955660.\n\nSubmitted - 2201.11710.pdf
", "abstract": "In this paper, we are interested in the performance of a variable-length stop-feedback (VLSF) code with m optimal decoding times for the binary-input additive white Gaussian noise channel. We first develop tight approximations to the tail probability of length-n cumulative information density. Building on the work of Yavas et al., for a given information density threshold, we formulate the integer program of minimizing the upper bound on average blocklength over all decoding times subject to the average error probability, minimum gap and integer constraints. Eventually, minimization of locally optimal upper bounds over all thresholds yields the globally minimum upper bound and the above method is called the two-step minimization. Relaxing to allow positive real-valued decoding times activates the gap constraint. We develop gap-constrained sequential differential optimization (SDO) procedure to find the optimal, gap-constrained, real-valued decoding times. In the error regime of practical interest, Polyanskiy's scheme of stopping at zero does not help. In this region, the achievability bounds estimated by the two-step minimization and gap-constrained SDO show that Polyanskiy's achievability bound for VLSF codes can be approached with a small number of decoding times.", "date": "2022-06-26", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "2327-2332", "id_number": "CaltechAUTHORS:20220804-765691000", "isbn": "978-1-6654-2159-1", "book_title": "2022 IEEE International Symposium on Information Theory (ISIT)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220804-765691000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1955660" } ] }, "doi": "10.1109/isit50566.2022.9834526", "primary_object": { "basename": "2201.11710.pdf", "url": "https://authors.library.caltech.edu/records/k6r2v-tvn68/files/2201.11710.pdf" }, "resource_type": "book_section", "pub_year": "2022", "author_list": "Yang, Hengjie; Yavas, Recep Can; et el." }, { "id": "https://authors.library.caltech.edu/records/e2ymt-8x707", "eprint_id": 112717, "eprint_status": "archive", "datestamp": "2023-08-20 05:38:35", "lastmod": "2023-10-23 22:43:54", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Yavas-Recep-Can", "name": { "family": "Yavas", "given": "Recep Can" }, "orcid": "0000-0002-5640-515X" }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Effros-M", "name": { "family": "Effros", "given": "Michelle" }, "orcid": "0000-0003-3757-0675" } ] }, "title": "Nested Sparse Feedback Codes for Point-to-Point, Multiple Access, and Random Access Channels", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2021 IEEE. \n\nThis work was supported in part by the National Science Foundation (NSF) under grant CCF-1817241 and CCF-1956386.", "abstract": "This paper investigates variable-length feedback codes for discrete memoryless channels in point-to-point, multiple access, and random access communication. The proposed nested code employs L decoding times n\u2081,n\u2082,\u2026,n_L for the point-to-point and multiple access channels and KL decoding times {n_(k,\u2113):1 \u2264 k \u2264 K,1 \u2264 \u2113 \u2264 L} for the random access channel with at most K active transmitters; in the latter case, decoding times n_(k,\u2113), 1 \u2264 \u2113 \u2264 L are reserved for decoding in the scenario where the decoder believes that the number of active transmitters is k. The code has a nested structure, i.e., codewords used to decode messages from k active transmitters are prefix of codewords used to decode messages from k+1 active transmitters. The code employs single-bit, scheduled feedback from the receiver to the transmitters at each potential decoding time to inform the transmitters whether or not it is able to decode. Transmitters cease transmission, thereby truncating their codewords, when no further transmissions are required by the decoder. The choice of decoding times is optimized to minimize the expected decoding time subject to an error probability constraint, and second order achievability bounds are derived.", "date": "2021-10-17", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "1-6", "id_number": "CaltechAUTHORS:20220105-510075300", "isbn": "978-1-6654-0312-2", "book_title": "2021 IEEE Information Theory Workshop (ITW)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220105-510075300", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1817241" }, { "agency": "NSF", "grant_number": "CCF-1956386" } ] }, "doi": "10.1109/itw48936.2021.9611385", "resource_type": "book_section", "pub_year": "2021", "author_list": "Yavas, Recep Can; Kostina, Victoria; et el." }, { "id": "https://authors.library.caltech.edu/records/bf3gq-1ke54", "eprint_id": 101308, "eprint_status": "archive", "datestamp": "2023-08-20 03:53:15", "lastmod": "2023-10-19 22:36:53", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Lin-Chung-Yi", "name": { "family": "Lin", "given": "Chung-Yi" } }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Hassibi-B", "name": { "family": "Hassibi", "given": "Babak" } } ] }, "title": "Differentially Quantized Gradient Descent", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2021 IEEE. \n\nThis work was supported in part by the National Science Foundation (NSF) under grants CCF-1751356, CCF-1956386, CNS-0932428, CCF-1018927, CCF-1423663 and CCF-1409204, by a grant from Qualcomm Inc., by NASAs Jet Propulsion Laboratory through the President and Directors Fund, and by King Abdullah University of Science and Technology. \n\nStimulating discussions with Dr. Himanshu Tyagi and Dr. Vincent Tan are gratefully acknowledged.\n\nAccepted Version - Differentially_Quantized_Gradient_Methods.pdf
Submitted - 2002.02508.pdf
", "abstract": "Consider the following distributed optimization scenario. A worker has access to training data that it uses to compute the gradients while a server decides when to stop iterative computation based on its target accuracy or delay constraints. The only information that the server knows about the problem instance is what it receives from the worker via a rate-limited noiseless communication channel. We introduce the technique we call differential quantization (DQ) that compensates past quantization errors to make the descent trajectory of a quantized algorithm follow that of its unquantized counterpart. Assuming that the objective function is smooth and strongly convex, we prove that differentially quantized gradient descent (DQ-GD) attains a linear convergence rate of max{\u03c3_(GD), \u03c1_n2^(-R)}, where \u03c3_(GD) is the convergence rate of unquantized gradient descent (GD), \u03c1_n is the covering efficiency of the quantizer, and R is the bitrate per problem dimension n. Thus at any R \u2265 log\u2082\u03c1_n/\u03c3_(GD), the convergence rate of DQ-GD is the same as that of unquantized GD, i.e., there is no loss due to quantization. We show a converse demonstrating that no GD-like quantized algorithm can converge faster than max{\u03c3_(GD), 2^(-R)}. Since quantizers exist with \u03c1_n \u2192 1 as n \u2192 \u221e (Rogers, 1963), this means that DQ-GD is asymptotically optimal. In contrast, naively quantized GD where the worker directly quantizes the gradient attains only \u03c3_(GD) + \u03c1_n2^(-R). The technique of differential quantization continues to apply to gradient methods with momentum such as Nesterov's accelerated gradient descent, and Polyak's heavy ball method. For these algorithms as well, if the rate is above a certain threshold, there is no loss in convergence rate obtained by the differentially quantized algorithm compared to its unquantized counterpart. Experimental results on both simulated and realworld least-squares problems validate our theoretical analysis.", "date": "2021-07", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "1200-1205", "id_number": "CaltechAUTHORS:20200214-105624458", "isbn": "978-1-5386-8209-8", "book_title": "2021 IEEE International Symposium on Information Theory (ISIT)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200214-105624458", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1751356" }, { "agency": "NSF", "grant_number": "CCF-1956386" }, { "agency": "NSF", "grant_number": "CNS-0932428" }, { "agency": "NSF", "grant_number": "CCF-1018927" }, { "agency": "NSF", "grant_number": "CCF-1423663" }, { "agency": "NSF", "grant_number": "CCF-1409204" }, { "agency": "Qualcomm Inc." }, { "agency": "JPL President and Director's Fund" }, { "agency": "King Abdullah University of Science and Technology (KAUST)" } ] }, "doi": "10.1109/ISIT45174.2021.9518254", "primary_object": { "basename": "2002.02508.pdf", "url": "https://authors.library.caltech.edu/records/bf3gq-1ke54/files/2002.02508.pdf" }, "related_objects": [ { "basename": "Differentially_Quantized_Gradient_Methods.pdf", "url": "https://authors.library.caltech.edu/records/bf3gq-1ke54/files/Differentially_Quantized_Gradient_Methods.pdf" } ], "resource_type": "book_section", "pub_year": "2021", "author_list": "Lin, Chung-Yi; Kostina, Victoria; et el." }, { "id": "https://authors.library.caltech.edu/records/ypd9p-p4p74", "eprint_id": 109928, "eprint_status": "archive", "datestamp": "2023-08-20 03:59:37", "lastmod": "2023-10-23 18:13:23", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sabag-Oron", "name": { "family": "Sabag", "given": "Oron" }, "orcid": "0000-0002-7907-1463" }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Hassibi-B", "name": { "family": "Hassibi", "given": "Babak" } } ] }, "title": "Feedback Capacity of MIMO Gaussian Channels", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2021 IEEE. \n\nThis work was supported in part by the National Science Foundation (NSF) under grants CCF-1751356 and CCF-1956386. O. Sabag is partially supported by the ISEF international postdoctoral fellowship.\n\nSubmitted - 2106.01994.pdf
", "abstract": "Finding a computable expression for the feedback capacity of channels with non-white Gaussian, additive noise is a long standing open problem. In this paper, we solve this problem in the scenario where the channel has multiple inputs and multiple outputs (MIMO) and the noise process is generated as the output of a state-space model (a hidden Markov model). The main result is a computable characterization of the feedback capacity as a finite-dimensional convex optimization problem. Our solution subsumes all previous solutions to the feedback capacity including the auto-regressive moving-average (ARMA) noise process of first order, even if it is a non-stationary process. The capacity problem can be viewed as the problem of maximizing the measurements' entropy rate of a controlled (policy-dependent) state-space subject to a power constraint. We formulate the finite-block version of this problem as a sequential convex optimization problem, which in turn leads to a single-letter and computable upper bound. By optimizing over a family of time-invariant policies that correspond to the channel inputs distribution, a tight lower bound is realized. We show that one of the optimization constraints in the capacity characterization boils down to a Riccati equation, revealing an interesting relation between explicit capacity formulae and Riccati equations.", "date": "2021-07", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "7-12", "id_number": "CaltechAUTHORS:20210719-210210078", "isbn": "978-1-5386-8209-8", "book_title": "2021 IEEE International Symposium on Information Theory", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210719-210210078", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1751356" }, { "agency": "NSF", "grant_number": "CCF-1956386" }, { "agency": "ISEF Foundation" } ] }, "doi": "10.1109/ISIT45174.2021.9518088", "primary_object": { "basename": "2106.01994.pdf", "url": "https://authors.library.caltech.edu/records/ypd9p-p4p74/files/2106.01994.pdf" }, "resource_type": "book_section", "pub_year": "2021", "author_list": "Sabag, Oron; Kostina, Victoria; et el." }, { "id": "https://authors.library.caltech.edu/records/788m1-51604", "eprint_id": 108537, "eprint_status": "archive", "datestamp": "2023-08-20 03:56:09", "lastmod": "2023-10-23 17:07:34", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Guo-Nian", "name": { "family": "Guo", "given": "Nian" }, "orcid": "0000-0003-4490-328X" }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" } ] }, "title": "Instantaneous SED coding over a DMC", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2021 IEEE. \n\nThis work was supported in part by the National Science Foundation (NSF) under grants CCF-1751356 and CCF-1956386. \n\nStimulating discussions with Prof. Richard Wesel, Amaael Antonini, and Prof. Aaron Wagner are gratefully acknowledged.\n\nSubmitted - 2103.08112.pdf
", "abstract": "In this paper, we propose a novel code for transmitting a sequence of n message bits in real time over a discrete-memoryless channel (DMC) with noiseless feedback, where the\nmessage bits stream into the encoder one by one at random time instants. Similar to existing posterior matching schemes with block encoding, the encoder in our work takes advantage of the channel feedback to form channel inputs that contain the information the decoder does not yet have, and that are distributed close to the capacity-achieving input distribution, but dissimilar to the existing posterior matching schemes, the encoder performs instantaneous encoding - it immediately weaves the new message bits into a continuing transmission. A posterior matching scheme by Naghshvar et al. partitions the source messages into groups so that the group posteriors have a small-enough difference (SED) to the capacity-achieving distribution, and transmits the group index that contains the actual message. Our code adopts the SED rule to apply to the evolving message alphabet that contains all the possible variable-length strings that the source could have emitted up to that time. Our instantaneous SED code achieves better delay-reliability tradeoffs than existing feedback codes over 2-input DMCs: we establish this dominance both by simulations and via an analysis comparing the performance of the instantaneous SED code to Burnashev's reliability function. Due to the message alphabet that grows exponentially with time t, the complexity of the instantaneous SED code is double-exponential in t. To overcome this complexity barrier to practical implementation, we design a low-complexity code for binary symmetric channels that we name the instantaneous type set SED code. It groups the message strings into sets we call type sets and tracks their prior and posterior probabilities jointly, resulting in the reduction of complexity from double-exponential to O(t\u2074). Simulation results show that the gap in performance between the instantaneous SED code and the instantaneous type-set SED code is negligible.", "date": "2021-07", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "148-153", "id_number": "CaltechAUTHORS:20210323-145545445", "isbn": "9781538682098", "book_title": "2021 IEEE International Symposium on Information Theory", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210323-145545445", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1751356" }, { "agency": "NSF", "grant_number": "CCF-1956386" } ] }, "doi": "10.1109/ISIT45174.2021.9518087", "primary_object": { "basename": "2103.08112.pdf", "url": "https://authors.library.caltech.edu/records/788m1-51604/files/2103.08112.pdf" }, "resource_type": "book_section", "pub_year": "2021", "author_list": "Guo, Nian and Kostina, Victoria" }, { "id": "https://authors.library.caltech.edu/records/7fn60-3nf98", "eprint_id": 108576, "eprint_status": "archive", "datestamp": "2023-08-20 03:56:24", "lastmod": "2023-10-23 17:09:22", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Yavas-Recep-Can", "name": { "family": "Yavas", "given": "Recep Can" }, "orcid": "0000-0002-5640-515X" }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Effros-M", "name": { "family": "Effros", "given": "Michelle" }, "orcid": "0000-0003-3757-0675" } ] }, "title": "Variable-length Feedback Codes with Several Decoding Times for the Gaussian Channel", "ispublished": "unpub", "full_text_status": "public", "keywords": "Variable-length stop-feedback codes, Gaussian channel, second-order achievability bound", "note": "\u00a9 2021 IEEE. \n\nThis work was supported in part by the National Science Foundation (NSF) under grant CCF-1817241 and CCF-1956386. \n\nStimulating discussions with Prof. Richard Wesel and Prof. Aaron Wagner are gratefully acknowledged.\n\nSubmitted - 2103.09373.pdf
", "abstract": "We investigate variable-length feedback (VLF) codes for the Gaussian point-to-point channel under maximal power, average error probability, and average decoding time constraints. Our proposed strategy chooses K < \u221e decoding times n\u2081,n\u2082,\u2026,n_K rather than allowing decoding at any time n = 0,1,2,\u2026. We consider stop-feedback, which is one-bit feedback transmitted from the receiver to the transmitter at times n\u2081,n\u2082,\u2026 only to inform her whether to stop. We prove an achievability bound for VLF codes with the asymptotic approximation ln M \u2248 NC(P)/1\u2212\u03f5 \u2212 \u221aN ln_((K\u22121))(N)V(P)/1\u2212\u03f5, where ln_((K))(\u22c5) denotes the K-fold nested logarithm function, N is the average decoding time, and C(P) and V(P) are the capacity and dispersion of the Gaussian channel, respectively. Our achievability bound evaluates a non-asymptotic bound and optimizes the decoding times n\u2081,\u2026,n_K within our code architecture.", "date": "2021-07", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "1883-1888", "id_number": "CaltechAUTHORS:20210329-152031630", "isbn": "978-1-5386-8209-8", "book_title": "2021 IEEE International Symposium on Information Theory", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210329-152031630", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1817241" }, { "agency": "NSF", "grant_number": "CCF-1956386" } ] }, "doi": "10.1109/ISIT45174.2021.9517993", "primary_object": { "basename": "2103.09373.pdf", "url": "https://authors.library.caltech.edu/records/7fn60-3nf98/files/2103.09373.pdf" }, "resource_type": "book_section", "pub_year": "2021", "author_list": "Yavas, Recep Can; Kostina, Victoria; et el." }, { "id": "https://authors.library.caltech.edu/records/kq0fn-m2245", "eprint_id": 107638, "eprint_status": "archive", "datestamp": "2023-08-20 00:41:47", "lastmod": "2023-10-23 16:04:43", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sabag-Oron", "name": { "family": "Sabag", "given": "Oron" }, "orcid": "0000-0002-7907-1463" }, { "id": "Tian-Peida", "name": { "family": "Tian", "given": "Peida" }, "orcid": "0000-0003-3665-8173" }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Hassibi-B", "name": { "family": "Hassibi", "given": "Babak" } } ] }, "title": "The Minimal Directed Information Needed to Improve the LQG Cost", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2020 IEEE. \n\nThis work was supported in part by the National Science Foundation (NSF) under grants CCF-1751356 and CCF-1956386. The work of O. Sabag is partially supported by the ISEF international postdoctoral fellowship.", "abstract": "We study a linear quadratic Gaussian (LQG) control problem, in which a noisy observation of the system state is available to the controller. To lower the achievable LQG cost, we introduce an extra communication link from the system to the controller. We investigate the trade-off between the improved LQG cost and the consumed communication (information) resources that are measured with the conditional directed information. The objective is to minimize the directed information over all encoding-decoding policies subject to a constraint on the LQG cost. The main result is a semidefinite programming formulation for the optimization problem in the finite-horizion scenario where the dynamical system may have time-varying parameters. This result extends the seminal work by Tanaka et al., where the direct noisy measurement of the system state at the controller is assumed to be absent. As part of our derivation to show the optimality of an encoder that transmits a Gaussian measurement of the state, we show that the presence of the noisy measurements at the encoder can not reduce the minimal directed information, extending a prior result of Kostina and Hassibi to the vector case. Finally, we show that the results in the finite-horizon case can be extended to the infinite-horizon scenario when assuming a time-invariant system, but possibly a time-varying policy. We show that the solution for this optimization problem can be realized by a time-invariant policy whose parameters can be computed explicitly from a finite-dimensional semidefinite program.", "date": "2020-12", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "1842-1847", "id_number": "CaltechAUTHORS:20210121-152557490", "isbn": "9781728174471", "book_title": "2020 59th IEEE Conference on Decision and Control (CDC)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210121-152557490", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1751356" }, { "agency": "NSF", "grant_number": "CCF-1956386" }, { "agency": "ISEF Foundation" } ] }, "doi": "10.1109/cdc42340.2020.9304490", "resource_type": "book_section", "pub_year": "2020", "author_list": "Sabag, Oron; Tian, Peida; et el." }, { "id": "https://authors.library.caltech.edu/records/wqemh-tva22", "eprint_id": 100285, "eprint_status": "archive", "datestamp": "2023-08-19 21:34:06", "lastmod": "2023-10-18 19:49:18", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Hassibi-B", "name": { "family": "Hassibi", "given": "Babak" } } ] }, "title": "Fundamental limits of distributed tracking", "ispublished": "unpub", "full_text_status": "public", "keywords": "CEO problem, Berger-Tung bound, distributed source coding, causal rate-distortion theory, Gauss-Markov source, LQG control", "note": "\u00a9 2020 IEEE. \n\nThis work was supported in part by the National Science Foundation (NSF) under grants CCF-1751356 and CCF-1817241. The work of Babak Hassibi was supported in part by the NSF under grants CNS-0932428, CCF-1018927, CCF-1423663 and CCF-1409204, by a grant from Qualcomm Inc., by NASA's Jet Propulsion Laboratory through the President and Director's Fund, and by King Abdullah University of Science and Technology.\n\nSubmitted - 1910.02534.pdf
", "abstract": "Consider the following communication scenario. An n-dimensional source with memory is observed by K isolated encoders via parallel channels, who causally compress their observations to transmit to the decoder via noiseless rate-constrained links. At each time instant, the decoder receives K new codewords from the observers, combines them with the past received codewords, and produces a minimum- distortion estimate of the latest block of n source symbols. This scenario extends the classical one-shot CEO problem to multiple rounds of communication with communicators maintaining memory of the past.We prove a coding theorem showing that the minimum asymptotically (as n \u2192 \u221e) achievable sum rate required to achieve a target distortion is equal to the directed mutual information from the observers to the decoder minimized subject to the distortion constraint and the separate encoding constraint. For the Gauss-Markov source observed via K parallel AWGN channels, we solve that minimal directed mutual information problem, thereby establishing the minimum asymptotically achievable sum rate. Finally, we explicitly bound the rate loss due to a lack of communication among the observers; that bound is attained with equality in the case of identical observation channels.The general coding theorem is proved via a new nonasymptotic bound that uses stochastic likelihood coders and whose asymptotic analysis yields an extension of the Berger-Tung inner bound to the causal setting. The analysis of the Gaussian case is facilitated by reversing the channels of the observers.", "date": "2020-06", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "2438-2443", "id_number": "CaltechAUTHORS:20191213-102421150", "isbn": "978-1-7281-6432-8", "book_title": "2020 IEEE International Symposium on Information Theory (ISIT)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191213-102421150", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1751356" }, { "agency": "NSF", "grant_number": "CCF-1817241" }, { "agency": "NSF", "grant_number": "CNS-0932428" }, { "agency": "NSF", "grant_number": "CCF-1018927" }, { "agency": "NSF", "grant_number": "CCF-1423663" }, { "agency": "NSF", "grant_number": "CCF-1409204" }, { "agency": "Qualcomm Inc." }, { "agency": "JPL President and Director's Fund" }, { "agency": "King Abdullah University of Science and Technology (KAUST)" } ] }, "doi": "10.1109/ISIT44484.2020.9174006", "primary_object": { "basename": "1910.02534.pdf", "url": "https://authors.library.caltech.edu/records/wqemh-tva22/files/1910.02534.pdf" }, "resource_type": "book_section", "pub_year": "2020", "author_list": "Kostina, Victoria and Hassibi, Babak" }, { "id": "https://authors.library.caltech.edu/records/vzqv8-2gk64", "eprint_id": 101305, "eprint_status": "archive", "datestamp": "2023-08-19 21:34:33", "lastmod": "2023-10-19 22:36:41", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Yavas-R-C", "name": { "family": "Yavas", "given": "Recep Can" } }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Effros-M", "name": { "family": "Effros", "given": "Michelle" } } ] }, "title": "Gaussian Multiple and Random Access in the Finite Blocklength Regime", "ispublished": "unpub", "full_text_status": "public", "keywords": "Gaussian multiple access channel, Gaussian random access, third-order asymptotics, finite blocklength, maximum likelihood decoder, spherical distribution", "note": "\u00a9 2020 IEEE. \n\nThis work was supported in part by the National Science Foundation (NSF) under grant CCF-1817241.\n\nSubmitted - 2001.03867.pdf
", "abstract": "This paper presents finite-blocklength achievabil- ity bounds for the Gaussian multiple access channel (MAC) and random access channel (RAC) under average-error and maximal-power constraints. Using random codewords uniformly distributed on a sphere and a maximum likelihood decoder, the derived MAC bound on each transmitter's rate matches the MolavianJazi-Laneman bound (2015) in its first- and second-order terms, improving the remaining terms to \u00bd log n/n + O(1/n) bits per channel use. The result then extends to a RAC model in which neither the encoders nor the decoder knows which of K possible transmitters are active. In the proposed rateless coding strategy, decoding occurs at a time n t that depends on the decoder's estimate t of the number of active transmitters k. Single-bit feedback from the decoder to all encoders at each potential decoding time n_i, i \u2264 t, informs the encoders when to stop transmitting. For this RAC model, the proposed code achieves the same first-, second-, and third-order performance as the best known result for the Gaussian MAC in operation.", "date": "2020-06", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "3013-3018", "id_number": "CaltechAUTHORS:20200214-105613893", "isbn": "978-1-7281-6432-8", "book_title": "2020 IEEE International Symposium on Information Theory (ISIT)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200214-105613893", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1817241" } ] }, "doi": "10.1109/ISIT44484.2020.9174026", "primary_object": { "basename": "2001.03867.pdf", "url": "https://authors.library.caltech.edu/records/vzqv8-2gk64/files/2001.03867.pdf" }, "resource_type": "book_section", "pub_year": "2020", "author_list": "Yavas, Recep Can; Kostina, Victoria; et el." }, { "id": "https://authors.library.caltech.edu/records/fp7q1-qx705", "eprint_id": 101306, "eprint_status": "archive", "datestamp": "2023-08-19 21:34:42", "lastmod": "2023-10-19 22:36:46", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Guo-Nian", "name": { "family": "Guo", "given": "Nian" }, "orcid": "0000-0003-4490-328X" }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" } ] }, "title": "Optimal Causal Rate-Constrained Sampling for a Class of Continuous Markov Processes", "ispublished": "unpub", "full_text_status": "public", "keywords": "Causal lossy source coding, sequential estimation, event-triggered sampling, zero-delay coding", "note": "\u00a9 2020 IEEE. \n\nThis work was supported in part by the National Science Foundation (NSF) under grant CCF-1751356.\n\nSubmitted - 2002.01581.pdf
", "abstract": "Consider the following communication scenario. An encoder observes a stochastic process and causally decides when and what to transmit about it, under a constraint on bits transmitted per second. A decoder uses the received codewords to causally estimate the process in real time. The encoder and the decoder are synchronized in time. We aim to find the optimal encoding and decoding policies that minimize the end-to-end estimation mean-square error under the rate constraint. For a class of continuous Markov processes satisfying regularity conditions, we show that the optimal encoding policy transmits a 1-bit codeword once the process innovation passes one of two thresholds. The optimal decoder noiselessly recovers the last sample from the 1-bit codewords and codeword-generating time stamps, and uses it as the running estimate of the current process, until the next codeword arrives. In particular, we show the optimal causal code for the Ornstein-Uhlenbeck process and calculate its distortion-rate function.", "date": "2020-06", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "2456-2461", "id_number": "CaltechAUTHORS:20200214-105617315", "isbn": "978-1-7281-6432-8", "book_title": "2020 IEEE International Symposium on Information Theory (ISIT)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200214-105617315", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1751356" } ] }, "doi": "10.1109/ISIT44484.2020.9174333", "primary_object": { "basename": "2002.01581.pdf", "url": "https://authors.library.caltech.edu/records/fp7q1-qx705/files/2002.01581.pdf" }, "resource_type": "book_section", "pub_year": "2020", "author_list": "Guo, Nian and Kostina, Victoria" }, { "id": "https://authors.library.caltech.edu/records/nm80z-qzc03", "eprint_id": 105182, "eprint_status": "archive", "datestamp": "2023-08-19 21:42:06", "lastmod": "2023-10-20 21:26:47", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sabag-Oron", "name": { "family": "Sabag", "given": "Oron" }, "orcid": "0000-0002-7907-1463" }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Hassibi-B", "name": { "family": "Hassibi", "given": "Babak" } } ] }, "title": "Stabilizing Dynamical Systems with Fixed-Rate Feedback using Constrained Quantizers", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2020 IEEE. \n\nThis work was supported in part by the National Science Foundation (NSF) under grant CCF-1751356. The work of O. Sabag was partially supported by the ISEF postdoctoral fellowship.", "abstract": "The stabilization of unstable dynamical systems using rate-limited feedback links is investigated. In the scenario of a constant-rate link and a noise with unbounded support, the fundamental limit of communication is known, but no simple algorithm to achieve it exists. The main challenge in constructing an optimal scheme is to fully exploit the communication resources while occasionally signaling the controller that a special operation needs to be taken due to a large noise observation. In this work, we present a simple and explicit algorithm that stabilizes the dynamical system and achieves the fundamental limits of communication. The new idea is to use a constrained quantizer in which certain patterns of sequences are avoided throughout the quantization process. These patterns are preserved to signal the controller that a zoom-out operation should be initiated due to large noise observation. We show that the constrained quantizer has a negligible effect on the rate, so it achieves the fundamental limit of communication. Specifically, the rate-optimal algorithm is shown to stabilize any \u03b2-moment of the state if the noise has a bounded absolute (\u03b2 +\u03f5)-moment for some \u03f5 > 0 regardless of the other noise characteristics.", "date": "2020-06", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "2855-2860", "id_number": "CaltechAUTHORS:20200831-150243516", "isbn": "9781728164328", "book_title": "2020 IEEE International Symposium on Information Theory (ISIT)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200831-150243516", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1751356" }, { "agency": "Israel Scholarship Education Foundation" } ] }, "doi": "10.1109/isit44484.2020.9173929", "resource_type": "book_section", "pub_year": "2020", "author_list": "Sabag, Oron; Kostina, Victoria; et el." }, { "id": "https://authors.library.caltech.edu/records/7zj6p-b1g14", "eprint_id": 99090, "eprint_status": "archive", "datestamp": "2023-08-19 17:39:29", "lastmod": "2023-10-18 17:51:00", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Guo-Nian", "name": { "family": "Guo", "given": "Nian" }, "orcid": "0000-0003-4490-328X" }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" } ] }, "title": "Optimal Causal Rate-Constrained Sampling of the Wiener Process", "ispublished": "unpub", "full_text_status": "public", "keywords": "Causal lossy source coding, sequential estimation, sampling", "note": "\u00a9 2019 IEEE. \n\nThis work was supported in part by the National Science Foundation (NSF) under grant CCF-1751356.\n\nSubmitted - 1909.01317.pdf
", "abstract": "We consider the following communication scenario. An encoder causally observes the Wiener process and decides when and what to transmit about it. A decoder makes real-time estimation of the process using causally received codewords. We determine the causal encoding and decoding policies that jointly minimize the mean-square estimation error, under the long-term communication rate constraint of R bits per second. We show that an optimal encoding policy can be implemented as a causal sampling policy followed by a causal compressing policy. We prove that the optimal encoding policy samples the Wiener process once the innovation passes either \u221a(1/R) or \u2212\u221a(1/R), and compresses the sign of the innovation (SOI) using a 1-bit codeword. The SOI coding scheme achieves the operational distortion-rate function, which is equal to D^(op)(R)=1/(6R). Surprisingly, this is significantly better than the distortion-rate tradeoff achieved in the limit of infinite delay by the best non-causal code. This is because the SOI coding scheme leverages the free timing information supplied by the zero-delay channel between the encoder and the decoder. The key to unlock that gain is the event-triggered nature of the SOI sampling policy. In contrast, the distortion-rate tradeoffs achieved with deterministic sampling policies are much worse: we prove that the causal informational distortion-rate function in that scenario is as high as D_(DET)(R)=5/(6R). It is achieved by the uniform sampling policy with the sampling interval 1/R. In either case, the optimal strategy is to sample the process as fast as possible and to transmit 1-bit codewords to the decoder without delay.", "date": "2019-09", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "1090-1097", "id_number": "CaltechAUTHORS:20191004-133629184", "isbn": "978-1-7281-3151-1", "book_title": "2019 57th Annual Allerton Conference on Communication, Control, and Computing", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191004-133629184", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1751356" } ] }, "doi": "10.1109/ALLERTON.2019.8919710", "primary_object": { "basename": "1909.01317.pdf", "url": "https://authors.library.caltech.edu/records/7zj6p-b1g14/files/1909.01317.pdf" }, "resource_type": "book_section", "pub_year": "2019", "author_list": "Guo, Nian and Kostina, Victoria" }, { "id": "https://authors.library.caltech.edu/records/0rxrz-y4z09", "eprint_id": 101289, "eprint_status": "archive", "datestamp": "2023-08-19 17:09:29", "lastmod": "2023-10-19 22:35:59", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" } ] }, "title": "Rate loss in the Gaussian CEO problem", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Gaussian CEO problem, noisy source coding", "note": "\u00a9 2019 IEEE. \n\nThis work was supported in part by the National Science Foundation (NSF) under grant CCF-1751356.", "abstract": "We present a characterization of the Gaussian CEO rate region, in which the operational point at each boundary is characterized by one free parameter. That parameter determines the water level. Only those sensors whose observation noise is below that water level need to compress and transmit their data. Using that characterization, we present a simple (suboptimal) achievable region, expressed in terms of the difference between the noisy and the noiseless rate-distortion functions. Using that achievable region, we can explicitly bound the rate loss due to lack of cooperation among the compressors.", "date": "2019-08", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "1-5", "id_number": "CaltechAUTHORS:20200214-101154368", "isbn": "978-1-5386-6900-6", "book_title": "2019 IEEE Information Theory Workshop (ITW)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200214-101154368", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1751356" } ] }, "doi": "10.1109/ITW44776.2019.8988944", "resource_type": "book_section", "pub_year": "2019", "author_list": "Kostina, Victoria" }, { "id": "https://authors.library.caltech.edu/records/71bcr-ega64", "eprint_id": 99076, "eprint_status": "archive", "datestamp": "2023-08-19 16:38:16", "lastmod": "2023-10-18 17:50:22", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Tian-Peida", "name": { "family": "Tian", "given": "Peida" }, "orcid": "0000-0003-3665-8173" }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" } ] }, "title": "From Parameter Estimation to Dispersion of Nonstationary Gauss-Markov Processes", "ispublished": "unpub", "full_text_status": "public", "keywords": "Parameter estimation, maximum likelihood estimator, unstable processes, finite blocklength analysis, lossy compression,\nsources with memory, rate-distortion theory, covering in stochastic processes", "note": "\u00a9 2019 IEEE. \n\nThis research was supported in part by the National Science Foundation (NSF) under Grant CCF-1751356.\n\nSubmitted - 1907.00304.pdf
", "abstract": "This paper provides a precise error analysis for the maximum likelihood estimate \u00e2 (u) of the parameter a given samples u = (u 1 , \u2026 , u n )^\u22a4 drawn from a nonstationary Gauss-Markov process U i = aU i\u22121 + Z i , i \u2265 1, where a > 1, U 0 = 0, and Z i 's are independent Gaussian random variables with zero mean and variance \u03c3^2 . We show a tight nonasymptotic exponentially decaying bound on the tail probability of the estimation error. Unlike previous works, our bound is tight already for a sample size of the order of hundreds. We apply the new estimation bound to find the dispersion for lossy compression of nonstationary Gauss-Markov sources. We show that the dispersion is given by the same integral formula derived in our previous work [1] for the (asymptotically) stationary Gauss-Markov sources, i.e., |a| < 1. New ideas in the nonstationary case include a deeper understanding of the scaling of the maximum eigenvalue of the covariance matrix of the source sequence, and new techniques in the derivation of our estimation error bound.", "date": "2019-07", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "2044-2048", "id_number": "CaltechAUTHORS:20191004-100332992", "isbn": "9781538692912", "book_title": "2019 IEEE International Symposium on Information Theory (ISIT)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191004-100332992", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1751356" } ] }, "doi": "10.1109/isit.2019.8849797", "primary_object": { "basename": "1907.00304.pdf", "url": "https://authors.library.caltech.edu/records/71bcr-ega64/files/1907.00304.pdf" }, "resource_type": "book_section", "pub_year": "2019", "author_list": "Tian, Peida and Kostina, Victoria" }, { "id": "https://authors.library.caltech.edu/records/sds1e-msc86", "eprint_id": 94369, "eprint_status": "archive", "datestamp": "2023-08-19 16:27:12", "lastmod": "2023-10-20 17:54:46", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Chen-Shuqing", "name": { "family": "Chen", "given": "Shuqing" } }, { "id": "Effros-M", "name": { "family": "Effros", "given": "Michelle" } }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" } ] }, "title": "Lossless Source Coding in the Point-to-Point, Multiple Access, and Random Access Scenarios", "ispublished": "unpub", "full_text_status": "public", "keywords": "Lossless source coding, Slepian-Wolf, random access, finite blocklength, random coding, non-asymptotic information theory, Gaussian approximation", "note": "\u00a9 2019 IEEE. \n\nThis work is supported in part by the National Science Foundation under Grant CCF-1817241. The work of S. Chen is supported in part by the Oringer Fellowship Fund in Information Science and Technology.\n\nSubmitted - 1902.03366.pdf
", "abstract": "This paper treats point-to-point, multiple access and random access lossless source coding in the finite-blocklength regime. A random coding technique is developed, and its power in analyzing the third-order coding performance is demonstrated in all three scenarios. Results include a third-order-optimal characterization of the Slepian-Wolf rate region and a proof showing that for dependent sources, the independent encoders used by Slepian-Wolf codes can achieve the same third-order- optimal performance as a single joint encoder. The concept of random access source coding, which generalizes the multiple access scenario to allow for a subset of participating encoders that is unknown a priori to both the encoders and the decoder, is introduced. Contributions include a new definition of the probabilistic model for a random access-discrete multiple source, a general random access source coding scheme that employs a rateless code with sporadic feedback, and an analysis demonstrating via a random coding argument that there exists a deterministic code of the proposed structure that simultaneously achieves the third- order-optimal performance of Slepian-Wolf codes for all possible subsets of encoders.", "date": "2019-07", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "1692-1696", "id_number": "CaltechAUTHORS:20190402-132221601", "isbn": "978-1-5386-9291-2", "book_title": "2019 IEEE International Symposium on Information Theory (ISIT)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190402-132221601", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1817241" }, { "agency": "Oringer Fellowship, Caltech" } ] }, "doi": "10.1109/ISIT.2019.8849742", "primary_object": { "basename": "1902.03366.pdf", "url": "https://authors.library.caltech.edu/records/sds1e-msc86/files/1902.03366.pdf" }, "resource_type": "book_section", "pub_year": "2019", "author_list": "Chen, Shuqing; Effros, Michelle; et el." }, { "id": "https://authors.library.caltech.edu/records/yn2pt-y7v42", "eprint_id": 99080, "eprint_status": "archive", "datestamp": "2023-08-19 16:38:46", "lastmod": "2023-10-18 17:50:37", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Lalitha-A", "name": { "family": "Lalitha", "given": "Anusha" } }, { "id": "Khina-A", "name": { "family": "Khina", "given": "Anatoly" }, "orcid": "0000-0003-2359-1678" }, { "id": "Javidi-T", "name": { "family": "Javidi", "given": "Tara" } }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" } ] }, "title": "Real-time Binary Posterior Matching", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2019 IEEE. \n\nThe work of A. Lalitha and T. Javidi was supported in part by the National Science Foundation (NSF) under Grant CIF-1719133, CIF-1513883 and CIF 1448237. This work has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sk\u0142odowska-Curie grant agreement No 708932. The work of V. Kostina was supported in part by the NSF under Grant CCF-1566567 and Grant CCF-1751356. This work was done in part while A. Khina and V. Kostina were visiting the Simons Institute for the Theory of Computing.", "abstract": "We consider the problem of communications over the binary symmetric channel with feedback, where the information sequence is made available in a causal, possibly random, fashion. We develop a real-time variant of the renowned Horstein scheme and provide analytical guarantees for its error-probability exponential decay rate. We further use the scheme to stabilize an unstable control plant over a binary symmetric channel and compare the analytical guarantees with its empirical performance as well as with those of anytime-reliable codes.", "date": "2019-07", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "2239-2243", "id_number": "CaltechAUTHORS:20191004-100333333", "isbn": "9781538692912", "book_title": "2019 IEEE International Symposium on Information Theory (ISIT)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191004-100333333", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1719133" }, { "agency": "NSF", "grant_number": "CCF-1513883" }, { "agency": "NSF", "grant_number": "CCF-1448237" }, { "agency": "Marie Curie Fellowship", "grant_number": "708932" }, { "agency": "NSF", "grant_number": "CCF-1566567" }, { "agency": "NSF", "grant_number": "CCF-1751356" } ] }, "doi": "10.1109/isit.2019.8849479", "resource_type": "book_section", "pub_year": "2019", "author_list": "Lalitha, Anusha; Khina, Anatoly; et el." }, { "id": "https://authors.library.caltech.edu/records/2me5b-rcc98", "eprint_id": 92630, "eprint_status": "archive", "datestamp": "2023-08-19 13:05:13", "lastmod": "2023-10-20 15:55:41", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Peres-Yuval", "name": { "family": "Peres", "given": "Yuval" }, "orcid": "0000-0001-5456-6323" }, { "id": "Ranade-Gireeja", "name": { "family": "Ranade", "given": "Gireeja" }, "orcid": "0000-0002-6747-4492" }, { "id": "Sellke-Mark", "name": { "family": "Sellke", "given": "Mark" }, "orcid": "0000-0001-9166-8185" } ] }, "title": "Exact minimum number of bits to stabilize a linear system", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2018 IEEE. \n\n\nThis work was supported in part by the National Science Foundation (NSF) under Grant CCF-1751356, and by the Simons Institute for the Theory of Computing.\n\nSubmitted - 1807.07686.pdf
", "abstract": "We consider an unstable scalar linear stochastic system, X_(n + 1) = aX_n + Z_n \u2013 U_n.; where a \u2265 1 is the system gain, Z_n's are independent random variables with bounded \u03b1-th moments, and U_n'S are the control actions that are chosen by a controller who receives a single element of a finite set {1, \u2026, M} as its only information about system state X_i. We show that M = [a] + 1 is necessary and sufficient for \u00df- moment stability, for any \u00df < a. Our achievable scheme is a uniform quantizer of the zoom-in / zoom-out type. We analyze its performance using probabilistic arguments. We prove a matching converse using information-theoretic techniques. Our results generalize to vector systems, to systems with dependent Gaussian noise, and to the scenario in which a small fraction of transmitted messages is lost.", "date": "2018-12", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "453-458", "id_number": "CaltechAUTHORS:20190204-124407625", "isbn": "978-1-5386-1395-5", "book_title": "2018 IEEE Conference on Decision and Control (CDC)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190204-124407625", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1751356" }, { "agency": "Simons Institute for the Theory of Computing" } ] }, "doi": "10.1109/CDC.2018.8619156", "primary_object": { "basename": "1807.07686.pdf", "url": "https://authors.library.caltech.edu/records/2me5b-rcc98/files/1807.07686.pdf" }, "resource_type": "book_section", "pub_year": "2018", "author_list": "Kostina, Victoria; Peres, Yuval; et el." }, { "id": "https://authors.library.caltech.edu/records/2neck-c6m85", "eprint_id": 94290, "eprint_status": "archive", "datestamp": "2023-08-19 11:48:32", "lastmod": "2023-10-20 17:50:58", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Hassibi-B", "name": { "family": "Hassibi", "given": "Babak" } } ] }, "title": "Rate-cost tradeoffs in scalar LQG control and tracking with side information", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Linear stochastic control, LQG control, remote control, rate-distortion tradeoff, causal rate-distortion theory, Gauss-Markov source, real-time tracking, Wyner-Ziv rate-distortion function", "note": "\u00a9 2018 IEEE. \n\nThe work of Victoria Kostina was supported in part by the National Science Foundation (NSF) under grant CCF-1751356. The work of Babak Hassibi was supported in part by the NSF under grants CNS-0932428, CCF-1018927, CCF-1423663 and CCF-1409204, by a grant from Qualcomm Inc., by NASA's Jet Propulsion Laboratory through the President and Director's Fund, and by King Abdullah University of Science and Technology.", "abstract": "Consider a control problem in which a remote controller chooses its control action based on two kinds of information about the system state: the information it receives from the system via a rate-constrained feedback link, and side information - a noisy measurement of the system state it observes directly. The goal of the controller is to minimize a quadratic cost function in the state variables and control signal, known as the linear quadratic regulator (LQR). We study the fundamental tradeoff between the communication rate, the expected cost b and the quality of side information. Due to a separation principle between estimation and control, we focus on the tracking problem, where the goal is to track the system state rather than to control it. We introduce the causal rate-distortion function with side information at the decoder. It is expressed in terms of directed mutual information, and it extends the classical (noncausal) Wyner-Ziv rate-distortion function to real-time tracking problems with causality constraints and memory of the past at both encoder and decoder. We compute that function in the scalar linear Gaussian setting; we draw a link with the Kalman filter; we show that making side information available also at the encoder does not help to improve the optimal tradeoffs.", "date": "2018-10", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "421-428", "id_number": "CaltechAUTHORS:20190329-091228468", "isbn": "978-1-5386-6596-1", "book_title": "56th Annual Allerton Conference on Communication, Control, and Computing", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190329-091228468", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1751356" }, { "agency": "NSF", "grant_number": "CNS-0932428" }, { "agency": "NSF", "grant_number": "CCF-1018927" }, { "agency": "NSF", "grant_number": "CCF-1423663" }, { "agency": "NSF", "grant_number": "CCF-1409204" }, { "agency": "Qualcomm Inc." }, { "agency": "JPL President and Director's Fund" }, { "agency": "King Abdullah University of Science and Technology (KAUST)" } ] }, "doi": "10.1109/ALLERTON.2018.8635889", "resource_type": "book_section", "pub_year": "2018", "author_list": "Kostina, Victoria and Hassibi, Babak" }, { "id": "https://authors.library.caltech.edu/records/bkmsv-e3w75", "eprint_id": 92652, "eprint_status": "archive", "datestamp": "2023-08-19 09:37:55", "lastmod": "2023-10-20 15:56:43", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Nakahira-Yorie", "name": { "family": "Nakahira", "given": "Yorie" }, "orcid": "0000-0003-3324-4602" }, { "id": "Xiao-Fangzhou", "name": { "family": "Xiao", "given": "Fangzhou" }, "orcid": "0000-0002-5001-5644" }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Doyle-J-C", "name": { "family": "Doyle", "given": "John C." }, "orcid": "0000-0002-1828-2486" } ] }, "title": "Fundamental limits and achievable performance in biomolecular control", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2018 AACC.", "abstract": "Understanding how a biomolecular system achieves various control objectives via chemical reactions is of crucial importance in cell biology. However, unlike typical control problems where full information about the system is assumed to be known, typically, only a small portion of the entire biomolecular system can be characterized with certainty. In order to gain insights in these situations, we use control and information theory to derive the performance bounds when chemical species implement feedback control via the production rate or the degradation rate of chemical species. We expand the approach of the pioneering work of Lestas et al. to treat more general scenarios and derive explicit lower bounds on the achievable Fano factor of the controlled species. Our results suggest that control and sensing via the degradation rates, compared with those via the production rates, benefit from the additional design freedom to choose degradation efficiencies, in addition to previously considered signal rate, which helps to lower the Fano factor of the controlled species. We compare our lower bounds with achievable performance via simulation of chemical master equations.", "date": "2018-06", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "2707-2714", "id_number": "CaltechAUTHORS:20190205-081829763", "isbn": "978-1-5386-5428-6", "book_title": "2018 Annual American Control Conference (ACC)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190205-081829763", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.23919/ACC.2018.8430933", "resource_type": "book_section", "pub_year": "2018", "author_list": "Nakahira, Yorie; Xiao, Fangzhou; et el." }, { "id": "https://authors.library.caltech.edu/records/39wq3-bh561", "eprint_id": 91190, "eprint_status": "archive", "datestamp": "2023-08-19 09:35:38", "lastmod": "2023-10-19 22:15:41", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marsiglietti-A", "name": { "family": "Marsiglietti", "given": "Arnaud" }, "orcid": "0000-0002-7459-0547" }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" } ] }, "title": "New Connections Between the Entropy Power Inequality and Geometric Inequalities", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Entropy power inequality, reverse entropy power inequality, hyperplane conjecture", "note": "\u00a9 2018 IEEE. \n\nSupported by the Walter S. Baer and Jeri Weiss CMI Postdoctoral Fellowship. \n\nSupported in part by the National Science Foundation (NSF) under Grant CCF-1566567.", "abstract": "The entropy power inequality (EPI) has a fundamental role in Information Theory, and has deep connections with famous geometric inequalities. In particular, it is often compared to the Brunn-Minkowski inequality in convex geometry. In this article, we further strengthen the relationships between the EPI and geometric inequalities. Specifically, we establish an equivalence between a strong form of reverse EPI and the hyperplane conjecture, which is a long-standing conjecture in high-dimensional convex geometry. We also provide a simple proof of the hyperplane conjecture for a certain class of distributions, as a straightforward consequence of the EPI.", "date": "2018-06", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "1978-1982", "id_number": "CaltechAUTHORS:20181126-145018270", "isbn": "978-1-5386-4780-6", "book_title": "2018 IEEE International Symposium on Information Theory (ISIT)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181126-145018270", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Center for the Mathematics of Information, Caltech" }, { "agency": "NSF", "grant_number": "CCF-1566567" } ] }, "doi": "10.1109/ISIT.2018.8437604", "resource_type": "book_section", "pub_year": "2018", "author_list": "Marsiglietti, Arnaud and Kostina, Victoria" }, { "id": "https://authors.library.caltech.edu/records/v0epv-38978", "eprint_id": 91192, "eprint_status": "archive", "datestamp": "2023-08-19 09:35:54", "lastmod": "2023-10-19 22:15:52", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Effros-M", "name": { "family": "Effros", "given": "Michelle" } }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Yavas-R-C", "name": { "family": "Yavas", "given": "Recep Can" } } ] }, "title": "Random Access Channel Coding in the Finite Blocklength Regime", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2018 IEEE. \n\nThis material is based upon work supported by the National Science Foundation under Grant No. 1527524.\n\nSubmitted - 1801.09018.pdf
", "abstract": "Consider a random access communication scenario over a channel whose operation is defined for any number of possible transmitters. Inspired by the model recently introduced for the Multiple Access Channel (MAC) with a fixed, known number of transmitters by Polyanskiy, we assume that the channel is invariant to permutations on its inputs, and that all active transmitters employ identical encoders. Unlike Polyanskiy, we consider a scenario in which neither the transmitters nor the receiver know which or how many transmitters are active. We refer to this agnostic communication setup as the Random Access Channel, or RAC. Limited feedback is used to ensure that the collection of active transmitters remains fixed during each epoch. The decoder is tasked with determining from the channel output the number of active transmitters (k) and their messages but not which transmitter sent which message. The central result of this work demonstrates the achievability on a RAC of performance that is first-order optimal for the MAC in operation during each coding epoch. While prior multiple access schemes for a fixed number of transmitters require 2^k - 1 simultaneous threshold rules, the proposed scheme uses a single threshold rule and achieves the same dispersion.", "date": "2018-06", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "1261-1265", "id_number": "CaltechAUTHORS:20181126-150049870", "isbn": "978-1-5386-4780-6", "book_title": "2018 IEEE International Symposium on Information Theory (ISIT)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181126-150049870", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1527524" } ] }, "doi": "10.1109/ISIT.2018.8437831", "primary_object": { "basename": "1801.09018.pdf", "url": "https://authors.library.caltech.edu/records/v0epv-38978/files/1801.09018.pdf" }, "resource_type": "book_section", "pub_year": "2018", "author_list": "Effros, Michelle; Kostina, Victoria; et el." }, { "id": "https://authors.library.caltech.edu/records/jcvfv-d5402", "eprint_id": 91189, "eprint_status": "archive", "datestamp": "2023-08-19 09:35:30", "lastmod": "2023-10-19 22:15:32", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Peres-Yuval", "name": { "family": "Peres", "given": "Yuval" } }, { "id": "Ranade-Gireeja", "name": { "family": "Ranade", "given": "Gireeja" }, "orcid": "0000-0002-6747-4492" }, { "id": "Sellke-Mark", "name": { "family": "Sellke", "given": "Mark" } } ] }, "title": "Stabilizing a System with an Unbounded Random Gain Using Only Finitely Many Bits", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2018 IEEE. \n\nWe thank Mikl\u00f3s R\u00e1cz and Serdar Y\u00fcksel for interesting discussions regarding this problem.\n\nSubmitted - 1805.05535.pdf
", "abstract": "We study the stabilization of an unpredictable linear control system where the controller must act based on a rate-limited observation of the state. More precisely, we consider the system X_(n+1) = A_n X_n +W_n \u2013U_n, where the A_n's are drawn independently at random at each time n from a known distribution with unbounded support, and where the controller receives at most R bits about the system state at each time from an encoder. We provide a time-varying achievable strategy to stabilize the system in a second-moment sense with fixed, finite R. While our previous result provided a strategy to stabilize this system using a variable-rate code, this work provides an achievable strategy using a fixed-rate code. The strategy we employ to achieve this is time-varying and takes different actions depending on the value of the state. It proceeds in two modes: a normal mode (or zoom-in), where the realization of A_n is typical, and an emergency mode (or zoom-out), where the realization of A_n is exceptionally large.", "date": "2018-06", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "2256-2260", "id_number": "CaltechAUTHORS:20181126-144509160", "isbn": "978-1-5386-4780-6", "book_title": "2018 IEEE International Symposium on Information Theory (ISIT)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181126-144509160", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1109/ISIT.2018.8437548", "primary_object": { "basename": "1805.05535.pdf", "url": "https://authors.library.caltech.edu/records/jcvfv-d5402/files/1805.05535.pdf" }, "resource_type": "book_section", "pub_year": "2018", "author_list": "Kostina, Victoria; Peres, Yuval; et el." }, { "id": "https://authors.library.caltech.edu/records/2nzh3-36w85", "eprint_id": 91185, "eprint_status": "archive", "datestamp": "2023-08-19 09:34:58", "lastmod": "2023-10-19 22:15:08", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Tian-Peida", "name": { "family": "Tian", "given": "Peida" }, "orcid": "0000-0003-3665-8173" }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" } ] }, "title": "The Dispersion of the Gauss-Markov Source", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2018 IEEE. \n\nThis research was supported in part by the National Science Foundation (NSF) under Grant CCF-1566567.\n\nAccepted Version - 1804.09418.pdf
", "abstract": "The Gauss-Markov source produces U_i=aU_(i-1)+ Z_i for i \u2265 1, where U_0 = 0, |a| < 1 and Z_i ~ N(0, \u03c3^2) are i.i.d. Gaussian random variables. We consider lossy compression of a block of n samples of the Gauss-Markov source under squared error distortion. We obtain the Gaussian approximation for the Gauss-Markov source with excess-distortion criterion for any distortion d > 0, and we show that the dispersion has a reverse waterfilling representation. This is the first finite blocklength result for lossy compression of sources with memory. We prove that the finite blocklength rate-distortion function R(n, d, \u03b5) approaches the rate-distortion function R(d) as R(n, d, \u03b5) = R(d)+\u221a{[V(d)/n]}Q^(-1)(\u03b5)+o([1/(\u221an)]), where V(d) is the dispersion, \u03b5 \u2208 (0,1) is the excess-distortion probability, and Q^(-1) is the inverse of the Q-function. We give a reverse waterfilling integral representation for the dispersion V (d), which parallels that of the rate-distortion functions for Gaussian processes. Remarkably, for all 0 <; d \u2264 \u03c32/(1+|a|)^2 ,R(n, d, c) of the Gauss-Markov source coincides with that of Zi, the i.i.d. Gaussian noise driving the process, up to the second-order term. Among novel technical tools developed in this paper is a sharp approximation of the eigenvalues of the covariance matrix of n samples of the Gauss-Markov source, and a construction of a typical set using the maximum likelihood estimate of the parameter a based on n observations.", "date": "2018-06", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "1490-1494", "id_number": "CaltechAUTHORS:20181126-141849980", "isbn": "978-1-5386-4780-6", "book_title": "2018 IEEE International Symposium on Information Theory (ISIT)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181126-141849980", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1566567" } ] }, "doi": "10.1109/ISIT.2018.8437463", "primary_object": { "basename": "1804.09418.pdf", "url": "https://authors.library.caltech.edu/records/2nzh3-36w85/files/1804.09418.pdf" }, "resource_type": "book_section", "pub_year": "2018", "author_list": "Tian, Peida and Kostina, Victoria" }, { "id": "https://authors.library.caltech.edu/records/5d8b1-t5m45", "eprint_id": 84755, "eprint_status": "archive", "datestamp": "2023-08-19 05:51:32", "lastmod": "2023-10-18 16:40:14", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Khina-A", "name": { "family": "Khina", "given": "Anatoly" }, "orcid": "0000-0003-2359-1678" }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Khisti-A", "name": { "family": "Khisti", "given": "Ashish" }, "orcid": "0000-0002-2331-8965" }, { "id": "Hassibi-B", "name": { "family": "Hassibi", "given": "Babak" } } ] }, "title": "Sequential coding of Gauss-Markov sources with packet erasures and feedback", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2017 IEEE. \n\nThe work of A. Khina has received funding from the European\nUnion's Horizon 2020 research and innovation programme under the Marie Sk\u0142odowska-Curie grant agreement No 708932. The work of V. Kostina was supported in part by the National Science Foundation under Grant CCF-1566567. Ashish Khisti was supported by the Canada Research Chairs Program. The work of B. Hassibi was supported in part by the National Science Foundation under grants CNS-0932428, CCF-1018927, CCF-1423663 and CCF-1409204, by a grant from Qualcomm Inc., by NASA's Jet Propulsion Laboratory through the President and Director's Fund, by King Abdulaziz University, and by King Abdullah University of Science and Technology. \n\nThe authors thank Y. Su for valuable discussions.\n\nSubmitted - 1702.01779.pdf
", "abstract": "We consider the problem of sequential transmission of Gauss-Markov sources. We show that in the limit of large spatial block lengths, greedy compression with respect to the squared error distortion is optimal; that is, there is no tension between optimizing the distortion of the source in the current time instant and that of future times. We then extend this result to the case where at time t a random compression rate rt is allocated independently of the rate at other time instants. This, in turn, allows us to derive the optimal performance of sequential coding over packet-erasure channels with instantaneous feedback. For the case of packet erasures with delayed feedback, we connect the problem to that of compression with side information that is known at the encoder and may be known at the decoder \u2014 where the most recent packets serve as side information that may have been erased, and demonstrate that the loss due to a delay by one time unit is rather small.", "date": "2017-11", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "529-533", "id_number": "CaltechAUTHORS:20180209-081746219", "isbn": "978-1-5090-3098-9", "book_title": "2017 IEEE Information Theory Workshop (ITW)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180209-081746219", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "European Union Horizon 2020" }, { "agency": "Marie Curie Fellowship", "grant_number": "708932" }, { "agency": "NSF", "grant_number": "CCF-1566567" }, { "agency": "Canada Research Chairs Program" }, { "agency": "NSF", "grant_number": "CNS-0932428" }, { "agency": "NSF", "grant_number": "CCF-1018927" }, { "agency": "NSF", "grant_number": "CCF-1423663" }, { "agency": "NSF", "grant_number": "CCF-1409204" }, { "agency": "Qualcomm Inc." }, { "agency": "NASA/JPL President and Director's Fund" }, { "agency": "King Abdulaziz University" }, { "agency": "King Abdullah University of Science and Technology (KAUST)" } ] }, "doi": "10.1109/ITW.2017.8277955", "primary_object": { "basename": "1702.01779.pdf", "url": "https://authors.library.caltech.edu/records/5d8b1-t5m45/files/1702.01779.pdf" }, "resource_type": "book_section", "pub_year": "2017", "author_list": "Khina, Anatoly; Kostina, Victoria; et el." }, { "id": "https://authors.library.caltech.edu/records/6h641-c9g43", "eprint_id": 80529, "eprint_status": "archive", "datestamp": "2023-08-19 03:24:35", "lastmod": "2023-10-17 16:04:25", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marsiglietti-A", "name": { "family": "Marsiglietti", "given": "Arnaud" }, "orcid": "0000-0002-7459-0547" }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" } ] }, "title": "A lower bound on the differential entropy for log-concave random variables with applications to rate-distortion theory", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Differential entropy, rate-distortion function, Shannon lower bound, log-concave distribution", "note": "\u00a9 2017 IEEE. \n\n[AM] Supported by the Walter S. Baer and Jeri Weiss CMI Postdoctoral Fellowship. [VK] Supported in part by the National Science Foundation (NSF) under Grant CCF-1566567.", "abstract": "We derive a lower bound on the differential entropy for symmetric log-concave random variable X in terms of the p-th absolute moment of X, which shows that entropy and p-th absolute moment of a symmetric log-concave random variable are comparable. We apply our bound to study the rate distortion function under distortion measure |x \u2212 x|^r for sources that follow a log-concave probability distribution. In particular, we establish that the difference between the rate distortion function and the Shannon lower bound is at most log(\u221a2e) \u2248 1.9 bits, independently of r and the target distortion d. For mean-square error distortion, the difference is at most log \u221a\u03c0e \u2248 1.55 bits, regardless of d. Our results generalize to the case of vector X. Our proof technique leverages tools from convex geometry.", "date": "2017-06", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "46-50", "id_number": "CaltechAUTHORS:20170816-162727008", "isbn": "978-1-5090-4096-4", "book_title": "2017 IEEE International Symposium on Information Theory (ISIT)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170816-162727008", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Walter S. Baer and Jeri Weiss CMI Postdoctoral Fellowship" }, { "agency": "NSF", "grant_number": "CCF-1566567" } ] }, "doi": "10.1109/ISIT.2017.8006487", "resource_type": "book_section", "pub_year": "2017", "author_list": "Marsiglietti, Arnaud and Kostina, Victoria" }, { "id": "https://authors.library.caltech.edu/records/fbjz6-23e82", "eprint_id": 80532, "eprint_status": "archive", "datestamp": "2023-08-19 03:24:51", "lastmod": "2023-10-17 16:04:36", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Noorzad-P", "name": { "family": "Noorzad", "given": "Parham" }, "orcid": "0000-0002-0201-3791" }, { "id": "Effros-M", "name": { "family": "Effros", "given": "Michelle" } }, { "id": "Langberg-M", "name": { "family": "Langberg", "given": "Michael" }, "orcid": "0000-0002-7470-0718" }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" } ] }, "title": "The birthday problem and zero-error list codes", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2017 IEEE. \n\nThis material is based upon work supported by the National Science Foundation under Grant Numbers 1321129, 1527524, and 1526771. \n\nThe first author thanks Ming Fai Wong for helpful discussions regarding an earlier version of Theorem 2.\n\nSubmitted - 1802.04719.pdf
", "abstract": "As an attempt to bridge the gap between classical information theory and the combinatorial world of zero-error information theory, this paper studies the performance of randomly generated codebooks over discrete memoryless channels under a zero-error constraint. This study allows the application of tools from one area to the other. Furthermore, it leads to an information-theoretic formulation of the birthday problem, which is concerned with the probability that in a given population, a fixed number of people have the same birthday. Due to the lack of a closed-form expression for this probability when the distribution of birthdays is not uniform, the resulting computation is not feasible in some applications; the information-theoretic formulation, however, can be analyzed for all distributions.", "date": "2017-06", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "1648-1652", "id_number": "CaltechAUTHORS:20170816-163747105", "isbn": "978-1-5090-4096-4", "book_title": "2017 IEEE International Symposium on Information Theory (ISIT)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170816-163747105", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1321129" }, { "agency": "NSF", "grant_number": "CCF-1527524" }, { "agency": "NSF", "grant_number": "CCF-1526771" } ] }, "doi": "10.1109/ISIT.2017.8006809", "primary_object": { "basename": "1802.04719.pdf", "url": "https://authors.library.caltech.edu/records/fbjz6-23e82/files/1802.04719.pdf" }, "resource_type": "book_section", "pub_year": "2017", "author_list": "Noorzad, Parham; Effros, Michelle; et el." }, { "id": "https://authors.library.caltech.edu/records/7f9ff-a2z55", "eprint_id": 80526, "eprint_status": "archive", "datestamp": "2023-08-19 03:24:20", "lastmod": "2023-10-17 16:04:13", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Tuncel-E", "name": { "family": "Tuncel", "given": "Ertem" }, "orcid": "0000-0001-9002-7562" } ] }, "title": "The rate-distortion function for successive refinement of abstract sources", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2017 IEEE. \n\nThis work was supported in part by the National Science Foundation (NSF) under Grant CCF-1566567.\n\nSubmitted - 1707.09567.pdf
", "abstract": "In successive refinement of information, the decoder refines its representation of the source progressively as it receives more encoded bits. The rate-distortion region of successive refinement describes the minimum rates required to attain the target distortions at each decoding stage. In this paper, we derive a parametric characterization of the rate-distortion region for successive refinement of abstract sources. Our characterization extends Csiszar's result [1] to successive refinement, and generalizes a result by Tuncel and Rose [2], applicable for finite alphabet sources, to abstract sources. The new characterization leads to a family of outer bounds to the rate-distortion region. It also enables new nonasymptotic converse bounds.", "date": "2017-06", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "1923-1927", "id_number": "CaltechAUTHORS:20170816-161319771", "isbn": "978-1-5090-4096-4", "book_title": "2017 IEEE International Symposium on Information Theory (ISIT)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170816-161319771", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1566567" } ] }, "doi": "10.1109/ISIT.2017.8006864", "primary_object": { "basename": "1707.09567.pdf", "url": "https://authors.library.caltech.edu/records/7f9ff-a2z55/files/1707.09567.pdf" }, "resource_type": "book_section", "pub_year": "2017", "author_list": "Kostina, Victoria and Tuncel, Ertem" }, { "id": "https://authors.library.caltech.edu/records/s1p2j-r3e02", "eprint_id": 73308, "eprint_status": "archive", "datestamp": "2023-08-19 00:39:54", "lastmod": "2023-10-24 15:12:50", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Khina-A", "name": { "family": "Khina", "given": "Anatoly" }, "orcid": "0000-0003-2359-1678" }, { "id": "Pettersson-G-M", "name": { "family": "Pettersson", "given": "Gustav M." }, "orcid": "0000-0002-4793-5212" }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Hassibi-B", "name": { "family": "Hassibi", "given": "Babak" } } ] }, "title": "Multi-rate control over AWGN channels via analog joint source-channel coding", "ispublished": "unpub", "full_text_status": "public", "keywords": "Channel coding, Signal to noise ratio, Distortion, Observers, AWGN channels, Receivers", "note": "\u00a9 2016 IEEE. \n\nThe work of A. Khina was supported in part by a Fulbright fellowship, Rothschild fellowship and has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sk\u0142lodowska-Curie grant agreement No 708932. \n\nThe work of G. M. Pettersson at Caltech was supported by The Boeing Company under the SURF program. \n\nThe work of B. Hassibi was supported in part by the National Science Foundation under grants CNS-0932428, CCF-1018927, CCF-1423663 and CCF-1409204, by a grant from Qualcomm Inc., by NASA's Jet Propulsion Laboratory through the President and Directors Fund, and by King Abdullah University of Science and Technology.\n\nSubmitted - 1609.07715v3.pdf
", "abstract": "We consider the problem of controlling an unstable plant over an additive white Gaussian noise (AWGN) channel with a transmit power constraint, where the signaling rate of communication is larger than the sampling rate (for generating observations and applying control inputs) of the underlying plant. Such a situation is quite common since sampling is done at a rate that captures the dynamics of the plant and which is often much lower than the rate that can be communicated. This setting offers the opportunity of improving the system performance by employing multiple channel uses to convey a single message (output plant observation or control input). Common ways of doing so are through either repeating the message, or by quantizing it to a number of bits and then transmitting a channel coded version of the bits whose length is commensurate with the number of channel uses per sampled message. We argue that such \"separated source and channel coding\" can be suboptimal and propose to perform joint source-channel coding. Since the block length is short we obviate the need to go to the digital domain altogether and instead consider analog joint source-channel coding. For the case where the communication signaling rate is twice the sampling rate, we employ the Archimedean bi-spiral-based Shannon-Kotel'nikov analog maps to show significant improvement in stability margins and linear-quadratic Gaussian (LQG) costs over simple schemes that employ repetition.", "date": "2016-12-29", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "5968-5973", "id_number": "CaltechAUTHORS:20170106-132902522", "isbn": "978-1-5090-1837-6", "book_title": "IEEE 55th Conference on Decision and Control (CDC)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170106-132902522", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Fulbright Foundation" }, { "agency": "Rothschild Foundation" }, { "agency": "Marie Curie Fellowship", "grant_number": "708932" }, { "agency": "Boeing Corporation" }, { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "NSF", "grant_number": "CNS-0932428" }, { "agency": "NSF", "grant_number": "CCF-1018927" }, { "agency": "NSF", "grant_number": "CCF-1423663" }, { "agency": "NSF", "grant_number": "CCF-1409204" }, { "agency": "Qualcomm Inc." }, { "agency": "JPL Director's Discretionary Fund" }, { "agency": "Caltech President's Fund" }, { "agency": "King Abdullah University of Science and Technology (KAUST)" } ] }, "doi": "10.1109/CDC.2016.7799185", "primary_object": { "basename": "1609.07715v3.pdf", "url": "https://authors.library.caltech.edu/records/s1p2j-r3e02/files/1609.07715v3.pdf" }, "resource_type": "book_section", "pub_year": "2016", "author_list": "Khina, Anatoly; Pettersson, Gustav M.; et el." }, { "id": "https://authors.library.caltech.edu/records/22nz5-yr497", "eprint_id": 74415, "eprint_status": "archive", "datestamp": "2023-08-20 13:39:10", "lastmod": "2023-10-24 22:36:57", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Hassibi-B", "name": { "family": "Hassibi", "given": "Babak" } } ] }, "title": "Rate-cost tradeoffs in control", "ispublished": "unpub", "full_text_status": "public", "keywords": "Linear stochastic control, rate-distortion tradeoff, high resolution, sequential rate-distortion theory, Shannon's lower bound", "note": "\u00a9 2016 IEEE. \n\nDate of Conference: 27-30 Sept. 2016. Date Added to IEEE Xplore: 13 February 2017. \n\nThe authors acknowledge many stimulating discussions with Dr. Anatoly Khina and his helpful comments on the earlier versions of the manuscript. The authors are also grateful to Ayush Pandey, who with incessant enthusiasm generated the plot in Fig. 2. The work of Victoria Kostina was supported in part by the National Science Foundation (NSF) under Grant CCF-1566567. The work of Babak Hassibi was supported in part by the National Science Foundation under grants CNS-0932428, CCF-1018927, CCF-1423663 and CCF-1409204, by a grant from Qualcomm Inc., by NASA's Jet Propulsion Laboratory through the President and Director's Fund, and by King Abdullah University of Science and Technology.\n\nSubmitted - 1612.02126.pdf
", "abstract": "Consider a distributed control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is minimize a quadratic cost function. The most basic special case of that cost function is the mean-square deviation of the system state from the desired state. We study the fundamental tradeoff between the communication rate r bits/sec and the limsup of the expected cost b, and show a lower bound on the rate necessary to attain b. The bound applies as long as the system noise has a probability density function. If target cost b is not too large, that bound can be closely approached by a simple lattice quantization scheme that only quantizes the innovation, that is, the difference between the controller's belief about the current state and the true state.", "date": "2016-09", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "1157-1164", "id_number": "CaltechAUTHORS:20170221-070702279", "isbn": "978-1-5090-4551-8", "book_title": "54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2016", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170221-070702279", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1566567" }, { "agency": "NSF", "grant_number": "CNS-0932428" }, { "agency": "NSF", "grant_number": "CCF-1018927" }, { "agency": "NSF", "grant_number": "CCF-1423663" }, { "agency": "NSF", "grant_number": "CCF-1409204" }, { "agency": "Qualcomm Inc." }, { "agency": "JPL President and Director's Fund" }, { "agency": "King Abdullah University of Science and Technology (KAUST)" } ] }, "doi": "10.1109/ALLERTON.2016.7852366", "primary_object": { "basename": "1612.02126.pdf", "url": "https://authors.library.caltech.edu/records/22nz5-yr497/files/1612.02126.pdf" }, "resource_type": "book_section", "pub_year": "2016", "author_list": "Kostina, Victoria and Hassibi, Babak" }, { "id": "https://authors.library.caltech.edu/records/wtp2v-v5192", "eprint_id": 74414, "eprint_status": "archive", "datestamp": "2023-08-20 13:39:02", "lastmod": "2023-10-24 22:36:52", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Peres-Y", "name": { "family": "Peres", "given": "Yuval" } }, { "id": "R\u00e1cz-M-Z", "name": { "family": "R\u00e1cz", "given": "Mikl\u03ccs Z." } }, { "id": "Ranade-G", "name": { "family": "Ranade", "given": "Gireeja" } } ] }, "title": "Rate-limited control of systems with uncertain gain", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2016 IEEE. \n\nDate of Conference: 27-30 Sept. 2016. Date Added to IEEE Xplore: 13 February 2017. \n\nWe thank Philip Chou, Tam\u00e1s Linder, and Kartik Venkat for useful pointers and helpful discussions.", "abstract": "Controlling and stabilizing systems involves countering the impact of explicit communication constraints in addition to inherent system model parameter uncertainty and random noise. Here we use an information-theoretic approach to jointly tackle all three issues and understand their interactions. Our main result bounds the minimum communication rate required for the mean-square stability of a system with uncertain system gain. Moreover, our techniques extend to provide a finer characterization of the required rate when specific finite bounds on the second moment of the state are desired.", "date": "2016-09", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "1189-1196", "id_number": "CaltechAUTHORS:20170221-064842476", "isbn": "978-1-5090-4551-8", "book_title": "54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2016", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170221-064842476", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1109/ALLERTON.2016.7852370", "resource_type": "book_section", "pub_year": "2016", "author_list": "Kostina, Victoria; Peres, Yuval; et el." }, { "id": "https://authors.library.caltech.edu/records/6d44p-8eb95", "eprint_id": 74417, "eprint_status": "archive", "datestamp": "2023-08-20 13:39:16", "lastmod": "2023-10-24 22:37:02", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" } ] }, "title": "When is Shannon's lower bound tight at finite blocklength?", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Lossy source coding, rate-distortion function Shannon's lower bound, finite blocklength regime, dispersion", "note": "\u00a9 2016 IEEE. \n\nDate of Conference: 27-30 Sept. 2016. Date Added to IEEE Xplore: 13 February 2017. \n\nThis work was supported in part by the National Science Foundation (NSF) under Grant CCF-1566567, and by the Simons Institute for the Theory of Computing.", "abstract": "This paper formulates an abstract version of Shannon's lower bound that applies to abstract sources and arbitrary distortion measures and that recovers the classical Shannon lower bound as a special case. A necessary and sufficient condition for it to be attained exactly is presented. It is demonstrated that whenever that condition is met, the d-tilted information of the source adopts a simple, explicit representation that parallels Shannon's lower bound. That convenient representation simplifies the non-asymptotic analysis of achievable rate-distortion tradeoffs. In particular, if a memoryless source meets Shannon's lower bound with equality, then its rate-dispersion function is given simply by the varentropy of the source.", "date": "2016-09", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "982-989", "id_number": "CaltechAUTHORS:20170221-071301966", "isbn": "978-1-5090-4551-8", "book_title": "54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2016", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170221-071301966", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1566567" }, { "agency": "Simons Institute for the Theory of Computing" } ] }, "doi": "10.1109/ALLERTON.2016.7852341", "resource_type": "book_section", "pub_year": "2016", "author_list": "Kostina, Victoria" }, { "id": "https://authors.library.caltech.edu/records/aagnm-e8q41", "eprint_id": 66072, "eprint_status": "archive", "datestamp": "2023-08-20 08:02:52", "lastmod": "2023-10-18 17:07:01", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" } ] }, "title": "Data compression with low distortion and finite blocklength", "ispublished": "unpub", "full_text_status": "public", "keywords": "Lossy source coding, finite blocklength regime, rate-dispersion function, dispersion, low distortion, high resolution, Shannon's lower bound", "note": "\u00a9 2015 IEEE. \n\nThis work is supported by the Simons Institute for the Theory of Computing.\n\nSubmitted - 1510.02190v2.pdf
", "abstract": "This paper considers lossy source coding of n-dimensional continuous memoryless sources with low mean-square error distortion and shows a simple, explicit approximation to the minimum source coding rate. More precisely, a nonasymptotic version of Shannon's lower bound is presented. Lattice quantizers are shown to approach that lower bound, provided that the source density is smooth enough and the distortion is low, which implies that fine multidimensional lattice coverings are nearly optimal in the rate-distortion sense even at finite n. The achievability proof technique avoids both the usual random coding argument and the simplifying assumption of the presence of a dither signal.", "date": "2015-09", "date_type": "published", "publisher": "IEEE", "id_number": "CaltechAUTHORS:20160412-084329467", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160412-084329467", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Institute" } ] }, "doi": "10.1109/ALLERTON.2015.7447135", "primary_object": { "basename": "1510.02190v2.pdf", "url": "https://authors.library.caltech.edu/records/aagnm-e8q41/files/1510.02190v2.pdf" }, "resource_type": "book_section", "pub_year": "2015", "author_list": "Kostina, Victoria" }, { "id": "https://authors.library.caltech.edu/records/m7z12-mav37", "eprint_id": 60806, "eprint_status": "archive", "datestamp": "2023-09-22 22:28:05", "lastmod": "2023-10-23 23:22:44", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Polyanskiy-Y", "name": { "family": "Polyanskiy", "given": "Yury" } }, { "id": "Verd\u00fa-S", "name": { "family": "Verd\u00fa", "given": "Sergio" } } ] }, "title": "Joint source-channel coding with feedback", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2015 IEEE.\n\nThis work was supported in part by the National Science Foundation (NSF) under Grant CCF-1016625, by the NSF CAREER award under Grant CCF-1253205, and by the Center for Science of Information (CSoI), an NSF Science and Technology Center, under Grant CCF-0939370.\n\nSubmitted - 1501.07640.pdf
", "abstract": "This paper quantifies the fundamental limits of variable-length transmission of a general (possibly analog) source over a memoryless channel with noiseless feedback, under a distortion constraint. We consider excess distortion, average distortion and guaranteed distortion (d-semifaithful codes). In contrast to the asymptotic fundamental limit, a general conclusion is that allowing variable-length codes and feedback leads to a sizable improvement in the fundamental delay-distortion tradeoff.", "date": "2015-06", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "276-280", "id_number": "CaltechAUTHORS:20151006-111737876", "isbn": "978-1-4673-7704-1", "book_title": "2015 IEEE International Symposium on Information Theory", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20151006-111737876", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1016625" }, { "agency": "NSF", "grant_number": "CCF-1253205" }, { "agency": "Center for Science of Information (CSoI)" }, { "agency": "NSF", "grant_number": "CCF-0939370" } ] }, "doi": "10.1109/ISIT.2015.7282460", "primary_object": { "basename": "1501.07640.pdf", "url": "https://authors.library.caltech.edu/records/m7z12-mav37/files/1501.07640.pdf" }, "resource_type": "book_section", "pub_year": "2015", "author_list": "Kostina, Victoria; Polyanskiy, Yury; et el." }, { "id": "https://authors.library.caltech.edu/records/v9s2k-9w002", "eprint_id": 58689, "eprint_status": "archive", "datestamp": "2023-08-20 06:04:26", "lastmod": "2023-10-23 19:37:03", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Polyanskiy-Y", "name": { "family": "Polyanskiy", "given": "Yury" } }, { "id": "Verd\u00fa-S", "name": { "family": "Verd\u00fa", "given": "Sergio" } } ] }, "title": "Transmitting k samples over the Gaussian channel: Energy-distortion tradeoff", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2015 IEEE.\n\nThis work was supported in part by the National Science Foundation (NSF)\nunder Grant CCF-1016625, by the NSF CAREER award under Grant CCF-1253205, and by the Center for Science of Information (CSoI), an NSF\nScience and Technology Center, under Grant CCF-0939370.", "abstract": "We investigate the minimum transmitted energy required to reproduce k source samples with a given fidelity after transmission over a memoryless Gaussian channel. In particular, we analyze the reduction in transmitted energy that accrues thanks to the availability of noiseless feedback. Allowing a nonvanishing excess distortion probability \u2208 boosts the asymptotic fundamental limit by a factor of 1\u2212\u2208, with or without feedback. If feedback is available, achieving guaranteed distortion with finite average energy is possible.", "date": "2015-05", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "1-5", "id_number": "CaltechAUTHORS:20150630-073130634", "isbn": "978-1-4799-5524-4", "book_title": "2015 IEEE Information Theory Workshop", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150630-073130634", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1016625" }, { "agency": "NSF", "grant_number": "CCF-1253205" }, { "agency": "NSF", "grant_number": "CCF-0939370" } ] }, "doi": "10.1109/ITW.2015.7133162", "resource_type": "book_section", "pub_year": "2015", "author_list": "Kostina, Victoria; Polyanskiy, Yury; et el." }, { "id": "https://authors.library.caltech.edu/records/9b4vw-vgj18", "eprint_id": 72015, "eprint_status": "archive", "datestamp": "2023-08-20 04:49:54", "lastmod": "2023-10-23 17:47:12", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Verd\u00fa-S", "name": { "family": "Verd\u00fa", "given": "Sergio" } } ] }, "title": "The output distribution of good lossy source codes", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2015 IEEE. \n\nThe authors are grateful to Dr. Curt Schieler for helpful discussions.", "abstract": "This paper provides a necessary condition good rate-distortion codes must satisfy. Specifically, it is shown that as the blocklength increases, the distribution of the input given the output of a good lossy code converges to the distribution of the input given the output of the joint distribution achieving the rate-distortion function, in terms of the normalized conditional relative entropy. The result holds for stationary ergodic sources with subadditive distortion measures, both for fixed-length and variable-length compression. A similar necessary condition is given for lossy joint source-channel coding.", "date": "2015-02", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "id_number": "CaltechAUTHORS:20161115-082050134", "isbn": "978-1-4799-7195-4", "book_title": "2015 Information Theory and Applications Workshop (ITA)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161115-082050134", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1109/ITA.2015.7309005", "resource_type": "book_section", "pub_year": "2015", "author_list": "Kostina, Victoria and Verd\u00fa, Sergio" }, { "id": "https://authors.library.caltech.edu/records/hm21b-pgx94", "eprint_id": 59088, "eprint_status": "archive", "datestamp": "2023-08-20 01:43:10", "lastmod": "2023-10-23 20:03:25", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Polyanskiy-Y", "name": { "family": "Polyanskiy", "given": "Yury" } }, { "id": "Verd\u00fa-S", "name": { "family": "Verd\u00fa", "given": "Sergio" } } ] }, "title": "Variable-Length Compression Allowing Errors", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2015 IEEE.\n\nThis work was supported in part by the Center for Science of Information\n(CSoI), an NSF Science and Technology Center, under Grant CCF-0939370.\n\nSubmitted - 1402.0608.pdf
", "abstract": "This paper studies the fundamental limits of the minimum average length of variable-length compression when a nonzero error probability \u03b5 is tolerated. We give non-asymptotic bounds on the minimum average length in terms of Erokhin's rate-distortion function and we use those bounds to obtain a Gaussian approximation on the speed of approach to the limit which is quite accurate for all but small blocklengths: (1-\u03b5)kH(S) - \u221akV(S)/2\u03c0 e \u2013 (Q^(-1)(\u03b5))^2/2 where Q-1 (\u00b7) is the functional inverse of the Q-function and V (S) is the source dispersion. A nonzero error probability thus not only reduces the asymptotically achievable rate by a factor of 1-\u03b5, but also this asymptotic limit is approached from below, i.e. a larger source dispersion and shorter blocklengths are beneficial. Further, we show that variable-length lossy compression under excess distortion constraint also exhibits similar properties.", "date": "2014-07", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "2679-2683", "id_number": "CaltechAUTHORS:20150730-142923980", "isbn": "9781479951864", "book_title": "2014 IEEE International Symposium on Information Theory (ISIT)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150730-142923980", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-0939370" } ] }, "doi": "10.1109/ISIT.2014.6875320", "primary_object": { "basename": "1402.0608.pdf", "url": "https://authors.library.caltech.edu/records/hm21b-pgx94/files/1402.0608.pdf" }, "resource_type": "book_section", "pub_year": "2014", "author_list": "Kostina, Victoria; Polyanskiy, Yury; et el." }, { "id": "https://authors.library.caltech.edu/records/6q0tk-bj790", "eprint_id": 92868, "eprint_status": "archive", "datestamp": "2023-08-19 20:39:24", "lastmod": "2023-10-20 16:33:24", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Loyka-S", "name": { "family": "Loyka", "given": "Sergey" } }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Gagnon-F", "name": { "family": "Gagnon", "given": "Fran\u00e7ois" } } ] }, "title": "Convexity of error rates in digital communications under non-Gaussian noise", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2013 IEEE.\n\nSubmitted - 1304.8102.pdf
", "abstract": "Convexity properties of error rates of a class of decoders, including the ML/min-distance one as a special case, are studied for arbitrary constellations. Earlier results obtained for the AWGN channel are extended to a wide class of (non-Gaussian) noise densities, including unimodal and spherically-invariant noise. Under these broad conditions, symbol error rates are shown to be convex functions of the SNR in the high-SNR regime with an explicitly-determined threshold, which depends only on the constellation dimensionality and minimum distance, thus enabling an application of the powerful tools of convex optimization to such digital communication systems in a rigorous way. It is the decreasing nature of the noise power density around the decision region boundaries that insures the convexity of symbol error rates in the general case. The known high/low SNR bounds of the convexity/concavity regions are tightened and no further improvement is shown to be possible in general.", "date": "2013-07", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "41-45", "id_number": "CaltechAUTHORS:20190213-075441906", "isbn": "978-1-4799-0446-4", "book_title": "2013 IEEE International Symposium on Information Theory", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190213-075441906", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1109/ISIT.2013.6620184", "primary_object": { "basename": "1304.8102.pdf", "url": "https://authors.library.caltech.edu/records/6q0tk-bj790/files/1304.8102.pdf" }, "resource_type": "book_section", "pub_year": "2013", "author_list": "Loyka, Sergey; Kostina, Victoria; et el." }, { "id": "https://authors.library.caltech.edu/records/t9jqv-sx591", "eprint_id": 49531, "eprint_status": "archive", "datestamp": "2023-08-19 11:36:42", "lastmod": "2023-10-17 21:30:59", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Verd\u00fa-S", "name": { "family": "Verd\u00fa", "given": "Sergio" } } ] }, "title": "Lossy joint source-channel coding in the finite blocklength regime", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2012 IEEE. This work was supported in part by the National Science Foundation (NSF) under Grant CCF-1016625 and by the Center for Science of Information (CSoI), an NSF Science and Technology Center, under Grant CCF-0939370.\nThe first author was supported in part by the Natural Sciences and Engineering Research Council of Canada.\n\nSubmitted - 1209.1317v2.pdf
", "abstract": "This paper shows new tight finite-blocklength bounds for the best achievable lossy joint source-channel code rate, and demonstrates that joint source-channel code design brings considerable performance advantage over a separate one in the non-asymptotic regime. A joint source-channel code maps a block of k source symbols onto a length - n channel codeword, and the fidelity of reproduction at the receiver end is measured by the probability \u03f5 that the distortion exceeds a given threshold d. For memoryless sources and channels, it is demonstrated that the parameters of the best joint source-channel code must satisfy nC - kR(d) \u2248 \u221a(nV + kV(d)) Q^(-1) (\u03f5), where C and V are the channel capacity and dispersion, respectively; R(d) and V(d) are the source rate-distortion and rate-dispersion functions; and Q is the standard Gaussian complementary cdf.", "date": "2012-07", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "1553-1557", "id_number": "CaltechAUTHORS:20140910-101108253", "isbn": "978-1-4673-2580-6", "book_title": "2012 IEEE International Symposium on Information Theory Proceedings (ISIT)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140910-101108253", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1016625" }, { "agency": "NSF", "grant_number": "CCF-0939370" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" } ] }, "doi": "10.1109/ISIT.2012.6283533", "primary_object": { "basename": "1209.1317v2.pdf", "url": "https://authors.library.caltech.edu/records/t9jqv-sx591/files/1209.1317v2.pdf" }, "resource_type": "book_section", "pub_year": "2012", "author_list": "Kostina, Victoria and Verd\u00fa, Sergio" }, { "id": "https://authors.library.caltech.edu/records/0q5a9-a3711", "eprint_id": 49532, "eprint_status": "archive", "datestamp": "2023-08-19 10:09:27", "lastmod": "2023-10-17 21:31:06", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Verd\u00fa-S", "name": { "family": "Verd\u00fa", "given": "Sergio" } } ] }, "title": "A new converse in rate-distortion theory", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Converse, finite blocklength regime, joint source-channel coding, lossy source coding, memoryless sources, rate-distortion theory, Shannon theory", "note": "\u00a9 2012 IEEE.\n\nThis work was supported in part by the National Science Foundation (NSF)\nunder Grant CCF-1016625 and by the Center for Science of Information\n(CSoI), an NSF Science and Technology Center, under Grant CCF-0939370.\nThe first author was supported in part by the Natural Sciences and Engineering\nResearch Council of Canada.", "abstract": "This paper shows new finite-blocklength converse bounds applicable to lossy source coding as well as joint source-channel coding, which are tight enough not only to prove the strong converse, but to find the rate-dispersion functions in both setups. In order to state the converses, we introduce the d-tilted information, a random variable whose expectation and variance (with respect to the source) are equal to the rate-distortion and rate-dispersion functions, respectively.", "date": "2012-03", "date_type": "published", "publisher": "IEEE", "id_number": "CaltechAUTHORS:20140910-102046386", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140910-102046386", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1016625" }, { "agency": "NSF", "grant_number": "CCF-0939370" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" } ] }, "doi": "10.1109/CISS.2012.6310949", "resource_type": "book_section", "pub_year": "2012", "author_list": "Kostina, Victoria and Verd\u00fa, Sergio" }, { "id": "https://authors.library.caltech.edu/records/rnvhv-6k433", "eprint_id": 49543, "eprint_status": "archive", "datestamp": "2023-08-19 08:16:43", "lastmod": "2023-10-17 21:31:43", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Verd\u00fa-S", "name": { "family": "Verd\u00fa", "given": "Sergio" } } ] }, "title": "Fixed-length lossy compression in the finite blocklength regime: Gaussian source", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Shannon theory, lossy source coding, rate distortion, memoryless sources, Gaussian source, finite blocklength regime, achievability, converse, sphere covering", "note": "\u00a9 2011 IEEE. This research was supported in part by NSF under grants CCF-1016625\nand CCF 09-39370. The first author was supported in part by the Natural\nSciences and Engineering Research Council of Canada.", "abstract": "For an i.i.d. Gaussian source with variance \u03c3^2, we show that it is necessary to spend \u00bd ln \u03c3^2/d + 1/\u221a(2n) Q^(-1)(\u03b5) + O (ln n/n) nats per sample in order to reproduce n source samples within mean-square error d with probability at least 1 - \u03b5, where Q^(-1) (\u00b7) is the inverse of the standard Gaussian complementary cdf. The first-order term is the rate-distortion function of the Gaussian source, while the second-order term measures its stochastic variability. We derive new achievability and converse bounds that are valid at any blocklength and show that the second-order approximation is tightly wedged between them, thus providing a concise and accurate approximation of the minimum achievable source coding rate at a given fixed blocklength (unless the blocklength is very small).", "date": "2011-10", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "457-461", "id_number": "CaltechAUTHORS:20140910-112002771", "isbn": "978-1-4577-0438-3", "book_title": "2011 IEEE Information Theory Workshop (ITW)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140910-112002771", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1016625" }, { "agency": "NSF", "grant_number": "CCF 09-39370" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" } ] }, "doi": "10.1109/ITW.2011.6089501", "resource_type": "book_section", "pub_year": "2011", "author_list": "Kostina, Victoria and Verd\u00fa, Sergio" }, { "id": "https://authors.library.caltech.edu/records/1angy-6zw59", "eprint_id": 49541, "eprint_status": "archive", "datestamp": "2023-08-19 07:38:01", "lastmod": "2023-10-17 21:31:33", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Verd\u00fa-S", "name": { "family": "Verd\u00fa", "given": "Sergio" } } ] }, "title": "Fixed-length lossy compression in the finite blocklength regime: discrete memoryless sources", "ispublished": "unpub", "full_text_status": "public", "keywords": "Shannon theory, lossy source coding, rate distortion,\nmemoryless sources, finite blocklength regime, achievability,\nconverse.", "note": "\u00a9 2011 IEEE. This work was partially supported by NSF under grant CCF-1016625 and by the Center for Science of Information, an NSF Science and Technology Center, under grant agreement CCF-0939370. The first author was supported\nin part by the Natural Sciences and Engineering Research Council of Canada. Useful discussions with Dr. Yury Polyanskiy are gratefully acknowledged. In particular, Theorem 3 arose from discussions with him.\n\nSubmitted - 1102.3944v3.pdf
", "abstract": "This paper studies the minimum achievable source coding rate as a function of blocklength n and tolerable distortion level d. Tight general achievability and converse bounds are derived that hold at arbitrary fixed blocklength. For stationary memoryless sources with separable distortion, the minimum rate achievable is shown to be q closely approximated by R(d) + \u221av(d)/nQ^(-1)(\u03f5), where R(d) is the rate-distortion function, V (d) is the rate dispersion, a characteristic of the source which measures its stochastic variability, Q-1 (\u00b7) is the inverse of the standard Gaussian complementary cdf, and \u03f5 is the probability that the distortion exceeds d. The new bounds and the second-order approximation of the minimum achievable rate are evaluated for the discrete memoryless source with symbol error rate distortion. In this case, the second-order approximation reduces to R(d) + 1/2 log n/n if the source is non-redundant.", "date": "2011-08", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "41-45", "id_number": "CaltechAUTHORS:20140910-110253022", "isbn": "978-1-4577-0596-0", "book_title": "IEEE International Symposium on Information Theory (ISIT), 2011", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140910-110253022", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1016625" }, { "agency": "NSF", "grant_number": "CCF-0939370" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" } ] }, "doi": "10.1109/ISIT.2011.6034159", "primary_object": { "basename": "1102.3944v3.pdf", "url": "https://authors.library.caltech.edu/records/1angy-6zw59/files/1102.3944v3.pdf" }, "resource_type": "book_section", "pub_year": "2011", "author_list": "Kostina, Victoria and Verd\u00fa, Sergio" }, { "id": "https://authors.library.caltech.edu/records/cb2tk-s7879", "eprint_id": 49500, "eprint_status": "archive", "datestamp": "2023-08-19 07:37:52", "lastmod": "2023-10-17 21:29:26", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Loyka-S", "name": { "family": "Loyka", "given": "Sergey" } } ] }, "title": "Performance analysis of coded V-BLAST with optimum power and rate allocation", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2011 IEEE.", "abstract": "Several optimization strategies for instantaneous rate and/or power allocation in the coded V-BLAST are studied analytically. Outage probabilities and system capacities of these strategies in a spatial multiplexing system are compared under generic settings. Since the conventional waterfilling algorithm is suboptimal for the coded V-BLAST, a recently-proposed \"fractional waterfilling\" algorithm is studied, which simultaneously maximizes the system capacity and minimizes the outage probability. A comparative, closed-form performance analysis of this and other algorithms is presented, including bounds on the outage probability and its low-outage approximations. The fractional waterfilling algorithm attains the full MIMO channel diversity and outperforms the other algorithms by a wide margin.", "date": "2011-08", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "1851-1855", "id_number": "CaltechAUTHORS:20140909-140645304", "isbn": "978-1-4577-0596-0", "book_title": "2011 IEEE International Symposium on Information Theory Proceedings (ISIT)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140909-140645304", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1109/ISIT.2011.6033871", "resource_type": "book_section", "pub_year": "2011", "author_list": "Kostina, Victoria and Loyka, Sergey" }, { "id": "https://authors.library.caltech.edu/records/0qfw1-19024", "eprint_id": 49533, "eprint_status": "archive", "datestamp": "2023-08-19 06:25:00", "lastmod": "2024-01-13 16:08:58", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Duarte-M-F", "name": { "family": "Duarte", "given": "Marco F." } }, { "id": "Jafarpour-S", "name": { "family": "Jafarpour", "given": "Sina" } }, { "id": "Calderbank-R", "name": { "family": "Calderbank", "given": "Robert" } } ] }, "title": "The value of redundant measurement in compressed sensing", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Compressed sensing, quantization, democracy, saturation", "note": "\u00a9 2011 IEEE. This work was supported in part by NSF under grant DMS-0914892, by ONR under grant N00014-08-1-1110, and by AFOSR under grants FA9550-09-1-0643 and FA9550-09-1-0551. V. Kostina was supported in part by the Natural Sciences and Engineering Research Council of Canada. M. F. Duarte was supported in part by NSF Supplemental Funding DMS-0439872 to UCLA-IPAM,P.I.", "abstract": "The aim of compressed sensing is to recover attributes of sparse signals using very few measurements. Given an overall bit budget for quantization, this paper demonstrates that there is value to redundant measurement. The measurement matrices considered here are required to have the property that signal recovery is still possible even after dropping certain subsets of D measurements. It introduces the concept of a measurement matrix that is weakly democratic in the sense that the amount of information about the signal carried by each of the designated D-subsets is the same. Examples of deterministic measurement matrices that are weakly democratic are constructed by exponentiating codewords from the binary second order Reed Muller code. The value in rejecting D measurements that are on average larger, is to be able to provide a finer grid for vector quantization of the remaining measurements, even after discounting the original budget by the bits used to identify the reject set. Simulation results demonstrate that redundancy improves recovery SNR, sometimes by a wide margin. Optimum performance occurs when a significant fraction of measurements are rejected.", "date": "2011-05", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "3656-3659", "id_number": "CaltechAUTHORS:20140910-103127300", "isbn": "978-1-4577-0538-0", "book_title": "IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140910-103127300", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0914892" }, { "agency": "Office of Naval Research (ONR)", "grant_number": "N00014-08-1-1110" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-09-1-0643" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-09-1-0551" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" }, { "agency": "NSF", "grant_number": "DMS-0439872" } ] }, "doi": "10.1109/ICASSP.2011.5947143", "resource_type": "book_section", "pub_year": "2011", "author_list": "Kostina, Victoria; Duarte, Marco F.; et el." }, { "id": "https://authors.library.caltech.edu/records/1w7bv-7y855", "eprint_id": 49528, "eprint_status": "archive", "datestamp": "2023-08-19 02:43:01", "lastmod": "2024-01-13 16:08:56", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Loyka-S", "name": { "family": "Loyka", "given": "Sergey" } }, { "id": "Gagnon-F", "name": { "family": "Gagnon", "given": "Fran\u00e7ois" } }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" } ] }, "title": "Error Rates of Capacity-Achieving Codes Are Convex", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2010 Crown.\n\nPublished - 05513337.pdf
Submitted - 1004.2683.pdf
", "abstract": "Motivated by a wide-spread use of convex optimization techniques, convexity properties of bit error rate of the maximum likelihood detector operating in the AWGN channel are studied for arbitrary constellations and bit mappings, which also includes coding under maximum-likelihood decoding. Under this generic setting, the pairwise probability of error and bit error rate are shown to be convex functions of the SNR and noise power in the high SNR/low noise regime with explicitly-determined boundary. Any code, including capacity-achieving ones, whose decision regions include the hardened noise spheres (from the noise sphere hardening argument in the channel coding theorem) satisfies this high SNR requirement and thus has convex error rates in both SNR and noise power. We conjecture that all capacity-achieving codes have convex error rates.", "date": "2010-06", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "325-329", "id_number": "CaltechAUTHORS:20140910-094918979", "isbn": "978-1-4244-7890-3", "book_title": "2010 IEEE International Symposium on Information Theory", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140910-094918979", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1109/ISIT.2010.5513337", "primary_object": { "basename": "05513337.pdf", "url": "https://authors.library.caltech.edu/records/1w7bv-7y855/files/05513337.pdf" }, "related_objects": [ { "basename": "1004.2683.pdf", "url": "https://authors.library.caltech.edu/records/1w7bv-7y855/files/1004.2683.pdf" } ], "resource_type": "book_section", "pub_year": "2010", "author_list": "Loyka, Sergey; Gagnon, Fran\u00e7ois; et el." }, { "id": "https://authors.library.caltech.edu/records/x209s-a6625", "eprint_id": 49523, "eprint_status": "archive", "datestamp": "2023-08-20 01:53:50", "lastmod": "2024-01-13 16:08:54", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Loyka-S", "name": { "family": "Loyka", "given": "Sergey" } } ] }, "title": "Optimum Power and Rate Allocation for Coded V-BLAST", "ispublished": "unpub", "full_text_status": "public", "keywords": "Multi-antenna (MIMO) system, spatial multiplexing,\ncoded V-BLAST, power/rate allocation, waterfilling,\nperformance analysis", "note": "\u00a9 2009 IEEE.\n\nPublished - 05199297.pdf
Submitted - 1010.2789v1.pdf
", "abstract": "An analytical framework for minimizing the outage probability of a coded spatial multiplexing system while keeping the rate close to the capacity is developed. Based on this framework, specific strategies of optimum power and rate allocation for the coded V-BLAST architecture are obtained and its performance is analyzed. A fractional waterfilling algorithm, which is shown to optimize both the capacity and the outage probability of the coded V-BLAST, is proposed. Compact, closed-form expressions for the optimum allocation of the average power are given. The uniform allocation of average power is shown to be near optimum at moderate to high SNR for the coded V-BLAST with the average rate allocation (when per-stream rates are set to match the per-stream capacity). The results reported also apply to multiuser detection and channel equalization relying on successive interference cancelation.", "date": "2009-06", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "4528-4533", "id_number": "CaltechAUTHORS:20140910-091940642", "isbn": "978-1-4244-3434-3", "book_title": "IEEE International Conference on Communications (ICC 2009)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140910-091940642", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1109/ICC.2009.5199297", "primary_object": { "basename": "1010.2789v1.pdf", "url": "https://authors.library.caltech.edu/records/x209s-a6625/files/1010.2789v1.pdf" }, "related_objects": [ { "basename": "05199297.pdf", "url": "https://authors.library.caltech.edu/records/x209s-a6625/files/05199297.pdf" } ], "resource_type": "book_section", "pub_year": "2009", "author_list": "Kostina, Victoria and Loyka, Sergey" }, { "id": "https://authors.library.caltech.edu/records/p1qg0-re193", "eprint_id": 49518, "eprint_status": "archive", "datestamp": "2023-08-19 21:21:43", "lastmod": "2023-10-17 21:30:23", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Loyka-S", "name": { "family": "Loyka", "given": "Sergey" } } ] }, "title": "Performance Analysis of V-BLAST with Optimum Power Allocation", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2007 Crown Copyright.\n\nPublished - 04411200.pdf
", "abstract": "Comprehensive performance analysis of the unordered V-BLAST algorithm with various power allocation strategies is presented, which makes use of analytical tools and resorts to Monte-Carlo simulations for validation purposes only. High-SNR approximations for the optimized average block and total error rates are given. The SNR gain of optimization is rigorously defined and studied using analytical tools, including lower and upper bounds, high and low SNR approximations. The gain is upper bounded by the number of transmitters, for any modulation format and any type of fading This upper bound is achieved at high SNR by the considered optimization strategies. While the average optimization is less complex than the instantaneous one, its performance is almost as good at high SNR. A measure of robustness of the optimized algorithm is introduced and evaluated, including compact closed-form approximations. The optimized algorithm is shown to be robust to perturbations in individual and total transmit powers. Based on the algorithm robustness, a pre-set power allocation is suggested as a low-complexity alternative to the other optimization strategies, which exhibits only a minor loss in performance over the practical SNR range.", "date": "2007-11", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "1508-1513", "id_number": "CaltechAUTHORS:20140910-070612419", "isbn": "978-1-4244-1042-2", "book_title": "GLOBECOM 07", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140910-070612419", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1109/GLOCOM.2007.290", "primary_object": { "basename": "04411200.pdf", "url": "https://authors.library.caltech.edu/records/p1qg0-re193/files/04411200.pdf" }, "resource_type": "book_section", "pub_year": "2007", "author_list": "Kostina, Victoria and Loyka, Sergey" }, { "id": "https://authors.library.caltech.edu/records/4bmbx-3bs79", "eprint_id": 49505, "eprint_status": "archive", "datestamp": "2023-08-19 20:19:20", "lastmod": "2023-10-17 21:29:45", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Loyka-S", "name": { "family": "Loyka", "given": "Sergev" } }, { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Cagnon-F", "name": { "family": "Gagnon", "given": "Francois" } } ] }, "title": "Symbol Error Rates of Maximum-Likelihood Detector: Convex/Concave Behavior and Applications", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2007 IEEE.\n\nPublished - 04557176.pdf
Submitted - 0705.1187.pdf
", "abstract": "Convexity/concavity properties of symbol error rates (SER) of the maximum likelihood detector operating in the AWGN channel (non-fading and fading) are studied. Generic conditions are identified under which the SER is a convex/concave function of the SNR. Universal bounds for the SER 1st and 2nd derivatives are obtained, which hold for arbitrary constellations and are tight for some of them. Applications of the results are discussed, which include optimum power allocation in spatial multiplexing systems, optimum power/time sharing to decrease or increase (jamming problem) error rate, and implication for fading channels.", "date": "2007-06", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "2501-2505", "id_number": "CaltechAUTHORS:20140909-150741253", "isbn": "978-1-4244-1397-3", "book_title": "IEEE International Symposium on Information Theory (ISIT), 2007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140909-150741253", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1109/ISIT.2007.4557176", "primary_object": { "basename": "04557176.pdf", "url": "https://authors.library.caltech.edu/records/4bmbx-3bs79/files/04557176.pdf" }, "related_objects": [ { "basename": "0705.1187.pdf", "url": "https://authors.library.caltech.edu/records/4bmbx-3bs79/files/0705.1187.pdf" } ], "resource_type": "book_section", "pub_year": "2007", "author_list": "Loyka, Sergev; Kostina, Victoria; et el." }, { "id": "https://authors.library.caltech.edu/records/5yg31-m5j17", "eprint_id": 49508, "eprint_status": "archive", "datestamp": "2023-08-19 17:55:45", "lastmod": "2023-10-17 21:29:53", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Loyka-S", "name": { "family": "Loyka", "given": "Sergey" } } ] }, "title": "Transmit Power Allocation for the V-BLAST Algorithm", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2006 IEEE.\n\nPublished - 01644596.pdf
", "abstract": "Optimum power allocation for the V-BLAST algorithm, which is based on various criteria (average and instantaneous block and total error rates (BLER and TBER)), is considered. Closed-form solutions are derived for high-SNR case in a Rayleigh fading channel. They are shown to be robust to small variations in allocated power and average SNR. It is demonstrated that the optimization \"on average\" is only slightly worse than the instantaneous one, albeit the latter requires an instantaneous feedback and hence is of higher complexity. The generic upper-bound for the SNR gain of any power allocation technique is derived. The BLER and TBER optimization criteria result in the same performance. Power optimization (of unordered BLAST) and optimal ordering result in almost the same performance improvement at high SNR.", "date": "2006-06", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "165-168", "id_number": "CaltechAUTHORS:20140909-153041130", "isbn": "0-7803-9528-X", "book_title": "23rd Biennial Symposium on Communications", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140909-153041130", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1109/BSC.2006.1644596", "primary_object": { "basename": "01644596.pdf", "url": "https://authors.library.caltech.edu/records/5yg31-m5j17/files/01644596.pdf" }, "resource_type": "book_section", "pub_year": "2006", "author_list": "Kostina, Victoria and Loyka, Sergey" }, { "id": "https://authors.library.caltech.edu/records/dzqr6-7dm90", "eprint_id": 49510, "eprint_status": "archive", "datestamp": "2023-08-19 17:16:53", "lastmod": "2023-10-17 21:29:55", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kostina-V", "name": { "family": "Kostina", "given": "Victoria" }, "orcid": "0000-0002-2406-7440" }, { "id": "Loyka-S", "name": { "family": "Loyka", "given": "Sergey" } } ] }, "title": "On Optimization of the V-BLAST Algorithm", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2006 IEEE.\n\nPublished - 01649092.pdf
", "abstract": "Optimum power allocation for the V-BLAST algorithm, which is based on various criteria (average and instantaneous block and total error rates (BLER and TBER)), is considered. Closed-form expressions are derived for high-SNR case in a Rayleigh fading channel. It is demonstrated that, in that case, the optimization \"on average\" is almost identical to the instantaneous one (while the former requires only the feedback \"on average\", the latter requires instantaneous feedback and hence is of higher complexity). The BLER and TBER optimization criteria result in the same performance. Power optimization (of un-ordered BLAST) and optimal ordering result in the same performance improvement at high SNR.", "date": "2006-02", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "110-113", "id_number": "CaltechAUTHORS:20140909-154358392", "isbn": "1-4244-0092-9", "book_title": "2006 International Zurich Seminar on Communications", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140909-154358392", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1109/IZS.2006.1649092", "primary_object": { "basename": "01649092.pdf", "url": "https://authors.library.caltech.edu/records/dzqr6-7dm90/files/01649092.pdf" }, "resource_type": "book_section", "pub_year": "2006", "author_list": "Kostina, Victoria and Loyka, Sergey" } ]