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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 16:18:07 +0000On the Synthesis of Stochastic Flow Networks
https://resolver.caltech.edu/CaltechPARADISE:2010.ETR101
Authors: {'items': [{'id': 'Zhou-Hongchao', 'name': {'family': 'Zhou', 'given': 'Hongchao'}}, {'id': 'Chen-Ho-Lin', 'name': {'family': 'Chen', 'given': 'Ho-Lin'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2010
DOI: 10.48550/arXiv.1209.0724
A stochastic flow network is a directed graph with incoming edges (inputs) and outgoing edges (outputs), tokens enter through the input edges, travel stochastically in the network and can exit the network through the output edges. Each node in the network is a splitter, namely, a token can enter a node through an incoming edge and exit on one of the output edges according to a predefined probability distribution. We address the following synthesis question: Given a finite set of possible splitters and an arbitrary rational probability distribution, design a stochastic flow network, such that every token that enters the input edge will exit the outputs with the prescribed probability distribution.
The problem of probability synthesis dates back to von Neummann's 1951 work and was followed, among others, by Knuth and Yao in 1976, who demonstrated that arbitrary rational probabilities can be generated with tree networks; where minimizing the expected path length, the expected number of coin tosses in their paradigm, is the key consideration. Motivated by the synthesis of stochastic DNA based molecular systems, we focus on designing optimal size stochastic flow networks (the size of a network is the number of splitters). We assume that each splitter has two outgoing edges and is unbiased (probability 1/2 per output edge). We show that an arbitrary rational probability a/b with a ≤ b ≤ 2^n can be realized by a stochastic flow network of size n, we also show that this is optimal. We note that our stochastic flow networks have feedback (cycles in the network), in fact, we demonstrate that feedback improves the expressibility of stochastic flow networks, since without feedback only probabilities of the form a/2^n (a an integer) can be realized.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/tmtgy-rqv10On the Synthesis of Stochastic Flow Networks
https://resolver.caltech.edu/CaltechAUTHORS:20110331-132532031
Authors: {'items': [{'id': 'Zhou-Hongchao', 'name': {'family': 'Zhou', 'given': 'Hongchao'}}, {'id': 'Chen-Ho-Lin', 'name': {'family': 'Chen', 'given': 'Ho-Lin'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2010
DOI: 10.1109/ISIT.2010.5513754
A stochastic flow network is a directed graph with incoming edges (inputs) and outgoing edges (outputs), tokens enter through the input edges, travel stochastically in the network and can exit the network through the output edges. Each node in the network is a splitter, namely, a token can enter a node through an incoming edge and exit on one of the output edges according to a predefined probability distribution. We address the following synthesis question: Given a finite set of possible splitters and an arbitrary rational probability distribution, design a stochastic flow network, such that every token that enters the input edge will exit the outputs with the prescribed probability distribution. The problem of probability synthesis dates back to von Neummann's 1951 work and was followed, among others, by Knuth and Yao in 1976, who demonstrated that arbitrary rational probabilities can be generated with tree networks; where minimizing the expected path length, the expected number of coin tosses in their paradigm, is the key consideration. Motivated by the synthesis of stochastic DNA based molecular systems, we focus on designing optimal-sized stochastic flow networks (the size of a network is the number of splitters). We assume that each splitter has two outgoing edges and is unbiased (probability 1/2 per output edge). We show that an arbitrary rational probability a/b with a ≤ b ≤ 2^n can be realized by a stochastic flow network of size n, we also show that this is optimal. We note that our stochastic flow networks have feedback (cycles in the network), in fact, we demonstrate that feedback improves the expressibility of stochastic flow networks, since without feedback only probabilities of the form ^a/_2^n) (a an integer) can be realized.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hccfy-ah066Patterned cells for phase change memories
https://resolver.caltech.edu/CaltechAUTHORS:20170213-160905267
Authors: {'items': [{'id': 'Jiang-Anxiao-Andrew', 'name': {'family': 'Jiang', 'given': 'Anxiao (Andrew)'}}, {'id': 'Zhou-Hongchao', 'name': {'family': 'Zhou', 'given': 'Hongchao'}}, {'id': 'Wang-Zhiying', 'name': {'family': 'Wang', 'given': 'Zhiying'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2011
DOI: 10.1109/ISIT.2011.6033979
Phase-change memory (PCM) is an emerging nonvolatile memory technology that promises very high performance. It currently uses discrete cell levels to represent data, controlled by a single amorphous/crystalline domain in a cell. To improve data density, more levels per cell are needed. There exist a number of challenges, including cell programming noise, drifting of cell levels, and the high power requirement for cell programming. In this paper, we present a new cell structure called patterned cell, and explore its data representation schemes. Multiple domains per cell are used, and their connectivity is used to store data. We analyze its storage capacity, and study its error-correction capability and the construction of error-control codes.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dpzzx-7bf24Nonuniform Codes for Correcting Asymmetric Errors
https://resolver.caltech.edu/CaltechAUTHORS:20120406-093123448
Authors: {'items': [{'id': 'Zhou-Hongchao', 'name': {'family': 'Zhou', 'given': 'Hongchao'}}, {'id': 'Jiang-A', 'name': {'family': 'Jiang', 'given': 'Anxiao (Andrew)'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2011
DOI: 10.1109/ISIT.2011.6033689
Codes that correct asymmetric errors have important applications in storage systems, including optical disks and Read Only Memories. The construction of asymmetric error correcting codes is a topic that was studied extensively, however, the existing approach for code construction assumes that every codeword could sustain t asymmetric errors. Our main observation is that in contrast to symmetric errors, where the error probability of a codeword is context independent (since the error probability for 1s and 0s is identical), asymmetric errors are context dependent. For example, the all-1 codeword has a higher error probability than the all-0 codeword (since the only errors are 1 → 0). We call the existing codes uniform codes while we focus on the notion of nonuniform codes, namely, codes whose codewords can tolerate different numbers of asymmetric errors depending on their Hamming weights. The goal of nonuniform codes is to guarantee the reliability of every codeword, which is important in data storage to retrieve whatever one wrote in. We prove an almost explicit upper bound on the size of nonuniform asymmetric error correcting codes and present two general constructions. We also study the rate of nonuniform codes compared to uniform codes and show that there is a potential performance gain.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bk5h1-qa850Systematic Error-Correcting Codes for Rank Modulation
https://resolver.caltech.edu/CaltechPARADISE:2011.ETR112
Authors: {'items': [{'id': 'Zhou-Hongchao', 'name': {'family': 'Zhou', 'given': 'Hongchao'}}, {'id': 'Jiang-A-A', 'name': {'family': 'Jiang', 'given': 'Anxiao (Andrew)'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2011
DOI: 10.48550/arXiv.1310.6817
The rank modulation scheme has been proposed recently for efficiently writing and storing data in nonvolatile
memories. Error-correcting codes are very important for rank
modulation; however, existing results have bee limited.
In this work, we explore a new approach, systematic error-correcting codes for rank modulation. Systematic codes have the benefits of enabling efficient information retrieval and potentially supporting more efficient encoding and decoding procedures. We study systematic codes for rank modulation equipped with the Kendall's τ-distance. We present (k + 2, k) systematic codes for correcting one error, which have optimal rates unless perfect
codes exist. We also study the design of multi-error-correcting codes, and prove that for any 2 ≤ k < n, there always exists an (n,k) systematic code of minimum distance
n − k. Furthermore, we prove that for rank modulation, systematic codes achieve the same capacity as general error-correcting codes.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xp404-dac89Efficient Generation of Random Bits From Finite State Markov Chains
https://resolver.caltech.edu/CaltechAUTHORS:20120503-095551724
Authors: {'items': [{'id': 'Zhou-Hongchao', 'name': {'family': 'Zhou', 'given': 'Hongchao'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2012
DOI: 10.1109/TIT.2011.2175698
The problem of random number generation from an uncorrelated random source (of unknown probability distribution) dates back to von Neumann's 1951 work. Elias (1972) generalized von Neumann's scheme and showed how to achieve optimal efficiency in unbiased random bits generation. Hence, a natural question is what if the sources are correlated? Both Elias and Samuelson proposed methods for generating unbiased random bits in the case of correlated sources (of unknown probability distribution), specifically, they considered finite Markov chains. However, their proposed methods are not efficient or have implementation difficulties. Blum (1986) devised an algorithm for efficiently generating random bits from degree-2 finite Markov chains in expected linear time, however, his beautiful method is still far from optimality on information-efficiency. In this paper, we generalize Blum's algorithm to arbitrary degree finite Markov chains and combine it with Elias's method for efficient generation of unbiased bits. As a result, we provide the first known algorithm that generates unbiased random bits from an arbitrary finite Markov chain, operates in expected linear time and achieves the information-theoretic upper bound on efficiency.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hnf87-01v85Patterned Cells for Phase Change Memories
https://resolver.caltech.edu/CaltechAUTHORS:20120502-130441311
Authors: {'items': [{'id': 'Jiang-Anxiao-Andrew', 'name': {'family': 'Jiang', 'given': 'Anxiao (Andrew)'}}, {'id': 'Zhou-Hongchao', 'name': {'family': 'Zhou', 'given': 'Hongchao'}}, {'id': 'Wang-Zhiying', 'name': {'family': 'Wang', 'given': 'Zhiying'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2012
Phase-change memory (PCM) is an emerging nonvolatile memory technology that promises very high performance.
It currently uses discrete cell levels to represent data, controlled
by a single amorphous/crystalline domain in a cell. To improve
data density, more levels per cell are needed. There exist a number of challenges, including cell programming noise, drifting of
cell levels, and the high power requirement for cell programming.
In this paper, we present a new cell structure called patterned cell, and explore its data representation schemes. Multiple
domains per cell are used, and their connectivity is used to
store data. We analyze its storage capacity, and study its error-correction capability and the construction of error-control codes.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6n5zz-gsa64Systematic Error-Correcting Codes for Rank Modulation
https://resolver.caltech.edu/CaltechAUTHORS:20120828-151501177
Authors: {'items': [{'id': 'Zhou-Hongchao', 'name': {'family': 'Zhou', 'given': 'Hongchao'}}, {'id': 'Jiang-A-A', 'name': {'family': 'Jiang', 'given': 'Anxiao (Andrew)'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2012
DOI: 10.1109/ISIT.2012.6284106
The rank modulation scheme has been proposed recently for efficiently writing and storing data in nonvolatile memories. Error-correcting codes are very important for rank modulation, and they have attracted interest among researchers. In this work, we explore a new approach, systematic error-correcting codes for rank modulation. In an (n,k) systematic code, we use the permutation induced by the levels of n cells to store data, and the permutation induced by the first k cells (k < n) has a one-to-one mapping to information bits. Systematic codes have the benefits of enabling efficient information retrieval and potentially supporting more efficient encoding and decoding procedures. We study systematic codes for rank modulation equipped with the Kendall's τ-distance. We present (k + 2, k) systematic codes for correcting one error, which have optimal sizes unless perfect codes exist. We also study the design of multi-error-correcting codes, and prove that for any 2 ≤ k < n, there always exists an (n, k) systematic code of minimum distance n-k. Furthermore, we prove that for rank modulation, systematic codes achieve the same capacity as general error-correcting codes.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/92gz1-39x98Nonuniform Codes for Correcting Asymmetric Errors in Data Storage
https://resolver.caltech.edu/CaltechAUTHORS:20130617-115747407
Authors: {'items': [{'id': 'Zhou-Hongchao', 'name': {'family': 'Zhou', 'given': 'Hongchao'}}, {'id': 'Jiang-A-A', 'name': {'family': 'Jiang', 'given': 'Anxiao (Andrew)'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2013
DOI: 10.1109/TIT.2013.2241175
The construction of asymmetric error-correcting codes is a topic that was studied extensively, however; the existing approach for code construction assumes that every codeword should tolerate t asymmetric errors. Our main observation is that in contrast to symmetric errors, asymmetric errors are content dependent. For example, in Z-channels, the all-1 codeword is prone to have more errors than the all-0 codeword. This motivates us to develop nonuniform codes whose codewords can tolerate different numbers of asymmetric errors depending on their Hamming weights. The idea in a nonuniform codes' construction is to augment the redundancy in a content-dependent way and guarantee the worst case reliability while maximizing the code size. In this paper, we first study nonuniform codes for Z-channels, namely, they only suffer one type of errors, say 1→ 0. Specifically, we derive their upper bounds, analyze their asymptotic performances, and introduce two general constructions. Then, we extend the concept and results of nonuniform codes to general binary asymmetric channels, where the error probability for each bit from 0 to 1 is smaller than that from 1 to 0.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/y34mf-tx768Synthesis of Stochastic Flow Networks
https://resolver.caltech.edu/CaltechAUTHORS:20140627-103709955
Authors: {'items': [{'id': 'Zhou-Hongchao', 'name': {'family': 'Zhou', 'given': 'Hongchao'}}, {'id': 'Chen-Ho-Lin', 'name': {'family': 'Chen', 'given': 'Ho-Lin'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2014
DOI: 10.1109/TC.2012.270
A stochastic flow network is a directed graph with incoming edges (inputs) and outgoing edges (outputs), tokens enter through the input edges, travel stochastically in the network, and can exit the network through the output edges. Each node in the network is a splitter, namely, a token can enter a node through an incoming edge and exit on one of the output edges according to a predefined probability distribution. Stochastic flow networks can be easily implemented by beam splitters, or by DNA-based chemical reactions, with promising applications in optical computing, molecular computing and stochastic computing. In this paper, we address a fundamental synthesis question: Given a finite set of possible splitters and an arbitrary rational probability distribution, design a stochastic flow network, such that every token that enters the input edge will exit the outputs with the prescribed probability distribution. The problem of probability transformation dates back to von Neumann's 1951 work and was followed, among others, by Knuth and Yao in 1976. Most existing works have been focusing on the "simulation" of target distributions. In this paper, we design optimal-sized stochastic flow networks for "synthesizing" target distributions. It shows that when each splitter has two outgoing edges and is unbiased, an arbitrary rational probability ɑ/b with ɑ ≤ b ≤ 2^n can be realized by a stochastic flow network of size n that is optimal. Compared to the other stochastic systems, feedback (cycles in networks) strongly improves the expressibility of stochastic flow networks.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/edqx4-2j933Systematic Error-Correcting Codes for Rank Modulation
https://resolver.caltech.edu/CaltechAUTHORS:20150202-150301749
Authors: {'items': [{'id': 'Zhou-Hongchao', 'name': {'family': 'Zhou', 'given': 'Hongchao'}}, {'id': 'Schwartz-Moshe', 'name': {'family': 'Schwartz', 'given': 'Moshe'}, 'orcid': '0000-0002-1449-0026'}, {'id': 'Jiang-A-A', 'name': {'family': 'Jiang', 'given': 'Anxiao (Andrew)'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2014
DOI: 10.1109/TIT.2014.2365499
The rank-modulation scheme has been recently proposed for efficiently storing data in nonvolatile memories. In this paper, we explore [n, k, d] systematic error-correcting codes for rank modulation. Such codes have length n, k information symbols, and minimum distance d. Systematic codes have the benefits of enabling efficient information retrieval in conjunction with memory-scrubbing schemes. We study systematic codes for rank modulation under Kendall's T-metric as well as under the ℓ∞-metric. In Kendall's T-metric, we present [k + 2, k, 3] systematic codes for correcting a single error, which have optimal rates, unless systematic perfect codes exist. We also study the design of multierror-correcting codes, and provide a construction of [k + t + 1, k, 2t + 1] systematic codes, for large-enough k. We use nonconstructive arguments to show that for rank modulation, systematic codes achieve the same capacity as general error-correcting codes. Finally, in the ℓ∞-metric, we construct two [n, k, d] systematic multierror-correcting codes, the first for the case of d = 0(1) and the second for d = Θ(n). In the latter case, the codes have the same asymptotic rate as the best codes currently known in this metric.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/zcv5z-eg591Streaming Algorithms for Optimal Generation of Random Bits
https://resolver.caltech.edu/CaltechAUTHORS:20160120-102504919
Authors: {'items': [{'id': 'Zhou-Hongchao', 'name': {'family': 'Zhou', 'given': 'Hongchao'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2016
DOI: 10.48550/arXiv.1209.0730
Generating random bits from a source of biased coins (the biased is unknown) is a classical question that was originally studied by von Neumann. There are a number of known algorithms that have asymptotically optimal information efficiency, namely, the expected number of generated random bits per input bit is asymptotically close to the entropy of the source. However, only the original von Neumann algorithm has a 'streaming property' - it operates on a single input bit at a time and it generates random bits when possible, alas, it does not have an optimal information efficiency.
The main contribution of this paper is an algorithm that generates random bit streams from biased coins, uses bounded space and runs in expected linear time. As the size of the allotted space increases, the algorithm approaches the information-theoretic upper bound on efficiency. In addition, we discuss how to extend this algorithm to generate random bit streams from m-sided dice or correlated sources such as Markov chains.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/g02dz-15w91Efficiently Extracting Randomness from Imperfect Stochastic Processes
https://resolver.caltech.edu/CaltechAUTHORS:20160120-104324682
Authors: {'items': [{'id': 'Zhou-Hongchao', 'name': {'family': 'Zhou', 'given': 'Hongchao'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2016
DOI: 10.48550/arXiv.1209.0734
We study the problem of extracting a prescribed number of random bits by reading the smallest possible number of symbols from non-ideal stochastic processes. The related interval algorithm proposed by Han and Hoshi has asymptotically optimal performance; however, it assumes that the distribution of the input stochastic process is known. The motivation for our work is the fact that, in practice, sources of randomness have inherent correlations and are affected by measurement's noise. Namely, it is hard to obtain an accurate estimation of the distribution. This challenge was addressed by the concepts of seeded and seedless extractors that can handle general random sources with unknown distributions. However, known seeded and seedless extractors provide extraction efficiencies that are substantially smaller than Shannon's entropy limit. Our main contribution is the design of extractors that have a variable input-length and a fixed output length, are efficient in the consumption of symbols from the source, are capable of generating random bits from general stochastic processes and approach the information theoretic upper bound on efficiency.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hknk5-gcf87Balanced Modulation for Nonvolatile Memories
https://resolver.caltech.edu/CaltechAUTHORS:20160120-083936607
Authors: {'items': [{'id': 'Zhou-Hongchao', 'name': {'family': 'Zhou', 'given': 'Hongchao'}}, {'id': 'Jiang-A-A', 'name': {'family': 'Jiang', 'given': 'Anxiao (Andrew)'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2016
DOI: 10.48550/arXiv.1209.0744
This paper presents a practical writing/reading scheme in nonvolatile memories, called balanced modulation, for minimizing the asymmetric component of errors. The main idea is to encode data using a balanced error-correcting code. When reading information from a block, it adjusts the reading threshold such that the resulting word is also balanced or approximately balanced. Balanced modulation has suboptimal performance for any cell-level distribution and it can be easily implemented in the current systems of nonvolatile memories. Furthermore, we studied the construction of balanced error-correcting codes, in particular, balanced LDPC codes. It has very efficient encoding and decoding algorithms, and it is more efficient than prior construction of balanced error-correcting codes.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/d8zca-x3206A Universal Scheme for Transforming Binary Algorithms to Generate Random Bits from Loaded Dice
https://resolver.caltech.edu/CaltechAUTHORS:20160120-102042704
Authors: {'items': [{'id': 'Zhou-Hongchao', 'name': {'family': 'Zhou', 'given': 'Hongchao'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2016
DOI: 10.48550/arXiv.1209.0726
In this paper, we present a universal scheme for transforming an arbitrary algorithm for biased 2-face coins to generate random bits from the general source of an m-sided die, hence enabling the application of existing algorithms to general sources. In addition, we study approaches of efficiently generating a prescribed number of random bits from an arbitrary biased coin. This contrasts with most existing works, which typically assume that the number of coin tosses is fixed, and they generate a variable number of random bits.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/abqc2-0en96The Synthesis and Analysis of Stochastic Switching Circuits
https://resolver.caltech.edu/CaltechAUTHORS:20160203-092316194
Authors: {'items': [{'id': 'Zhou-Hongchao', 'name': {'family': 'Zhou', 'given': 'Hongchao'}}, {'id': 'Loh-Po-Ling', 'name': {'family': 'Loh', 'given': 'Po-Ling'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2016
DOI: 10.48550/arXiv.1209.0715
Stochastic switching circuits are relay circuits that
consist of stochastic switches called pswitches. The study of stochastic switching circuits has widespread applications in many fields of computer science, neuroscience, and biochemistry. In this paper, we discuss several properties of stochastic switching circuits, including robustness, expressibility, and probability approximation. First, we study the robustness, namely, the effect caused by introducing an error of size Є to each pswitch in a stochastic circuit. We analyze two constructions and prove that simple series-parallel circuits are robust to small error perturbations,
while general series-parallel circuits are not. Specifically, the total error introduced by perturbations of size less than Є is bounded by a constant multiple of Є in a simple series-parallel circuit, independent of the size of the circuit. Next, we study the expressibility of stochastic switching circuits: Given an integer q and a pswitch set S = {1/q,2/q,...,q-1/q}, can we synthesize any rational probability with denominator q^n (for arbitrary n) with a simple series-parallel stochastic switching
circuit? We generalize previous results and prove that when q is a multiple of 2 or 3, the answer is yes. We also show that when q is a prime number larger than 3, the answer is no. Probability approximation is studied for a general case of an arbitrary pswitch set S = {s_1, s_2,... , s_(|S|)}. In this case, we propose an algorithm based on local optimization to approximate any desired probability. The analysis reveals that the approximation error of a switching circuit decreases exponentially with an increasing circuit size.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/rzzjv-4hf17Stopping Set Elimination for LDPC Codes
https://resolver.caltech.edu/CaltechAUTHORS:20180125-132316726
Authors: {'items': [{'id': 'Jiang-Anxiao-Andrew', 'name': {'family': 'Jiang', 'given': 'Anxiao (Andrew)'}}, {'id': 'Upadhyaya-P', 'name': {'family': 'Upadhyaya', 'given': 'Pulakesh'}}, {'id': 'Wang-Ying', 'name': {'family': 'Wang', 'given': 'Ying'}}, {'id': 'Narayanan-K-R', 'name': {'family': 'Narayanan', 'given': 'Krishna R.'}}, {'id': 'Zhou-Hongchao', 'name': {'family': 'Zhou', 'given': 'Hongchao'}}, {'id': 'Sima-Jin', 'name': {'family': 'Sima', 'given': 'Jin'}, 'orcid': '0000-0003-4588-9790'}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2017
DOI: 10.1109/ALLERTON.2017.8262806
This work studies the Stopping-Set Elimination Problem, namely, given a stopping set, how to remove the fewest erasures so that the remaining erasures can be decoded by belief propagation in k iterations (including k =∞). The NP-hardness of the problem is proven. An approximation algorithm is presented for k = 1. And efficient exact algorithms are presented for general k when the stopping sets form trees.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vnf04-m3829Linear Transformations for Randomness Extraction
https://resolver.caltech.edu/CaltechAUTHORS:20191004-151746022
Authors: {'items': [{'id': 'Zhou-Hongchao', 'name': {'family': 'Zhou', 'given': 'Hongchao'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2019
DOI: 10.48550/arXiv.1209.0732
Information-efficient approaches for extracting randomness from imperfect sources have been extensively studied, but simpler and faster ones are required in the high-speed applications of random number generation. In this paper, we focus on linear constructions, namely, applying linear transformation for randomness extraction. We show that linear transformations based on sparse random matrices are asymptotically optimal to extract randomness from independent sources and bit-fixing sources, and they are efficient (may not be optimal) to extract randomness from hidden Markov sources. Further study demonstrates the flexibility of such constructions on source models as well as their excellent information-preserving capabilities. Since linear transformations based on sparse random matrices are computationally fast and can be easy to implement using hardware like FPGAs, they are very attractive in the high-speed applications. In addition, we explore explicit constructions of transformation matrices. We show that the generator matrices of primitive BCH codes are good choices, but linear transformations based on such matrices require more computational time due to their high densities.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/m07z5-rej76