Article records
https://feeds.library.caltech.edu/people/Zhou-Hongchao/article.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenSat, 13 Apr 2024 00:32:15 +0000Efficient 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.edu/records/hnf87-01v85Nonuniform 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.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.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.edu/records/zcv5z-eg591