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The minimax distortion redundancy in noisy source coding

IEEE TRANSACTIONS ON INFORMATION THEORY 2003年第11期49卷 3020-3030页

作者： Dembo, A Weissman, T Stanford Univ Dept Stat Stanford CA 94305 USA Stanford Univ Dept Math Stanford CA 94305 USA Technion Israel Inst Technol Dept Elect Engn IL-32000 Haifa Israel Hewlett Packard Labs Palo Alto CA USA

Consider the problem of finite-rate filtering of a discrete memoryless process {X-i}(igreater than or equal to1) based on its noisy observation sequence {Z(i)}(igreater than or equal to1), which is the output of a discrete memoryless channel (DMC) whose input is {X-i}(igreater than or equal to1). When the distribution of the pairs (X-i, Z(i)), P-X,P-Z, is known, and for a given distortion measure, the solution to this problem is well known to be given by classical rate-distortion theory upon the introduction of a modified distortion measure. In this work, we address the case where P-X,P-Z, rather than being completely specified, is only known to belong to some set Lambda. For a fixed encoding rate R, we look at the worst case, over all theta epsilon Lambda, of the difference between the expected distortion of a given scheme which is not allowed to depend on the active source theta epsilon Lambda and the value of the distortion-rate function at R corresponding to the noisy source theta. We study the minimum attainable value achievable by any scheme operating at rate R for this worst case quantity, denoted by D(Lambda, R). Linking this problem and that of source coding under several distortion measures, we prove a coding theorem for the latter problem and apply it to characterize D(Lambda, R) for the case where all members of Lambda share the same noisy marginal. For the case of a general Lambda, we obtain a single-letter characterization of D(Lambda, R) for the finite-alphabet case. This gives, in particular, a necessary and sufficient condition on the set Lambda for the existence of a coding scheme which is universally optimal for all members of Lambda and characterizes the approximation-estimation tradeoff for statistical modeling of noisy source coding problems. Finally, we obtain D(Lambda, R) in closed form for cases where Lambda consists of distributions on the (channel) input-output pair of a Bernoulli source corrupted by a binary-symmetric channel (BSC). In pa

关键词： approximation-estimation tradeoff denoising lossy source coding minimax distortion redundancy noisy sources

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Lossless source coding in the Point-to-Point, Multiple Access, and Random Access Scenarios

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IEEE TRANSACTIONS ON INFORMATION THEORY 2020年第11期66卷 6688-6722页

作者： Chen, Shuqing Effros, Michelle Kostina, Victoria CALTECH Dept Elect Engn Pasadena CA 91125 USA Virtu Financial Inc New York NY 10006 USA

This work studies point-to-point, multiple access, and random access lossless source coding in the finite-blocklength regime. In each scenario, a random coding technique is developed and used to analyze third-order coding performance. Asymptotic results include a third-order characterization of the Slepian-Wolf rate region with an improved converse that relies on a connection to composite hypothesis testing. For dependent sources, the result implies that 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 is introduced to generalize multiple access (Slepian-Wolf) source coding to the case where encoders decide independently whether or not to participate and the set of participating encoders is unknown a priori to both the encoders and the decoder. The proposed random access source coding strategy employs rateless coding with scheduled feedback. A random coding argument proves the existence of a single deterministic code of this structure that simultaneously achieves the third-order-optimal Slepian-Wolf performance for each possible active encoder set.

关键词： source coding Decoding Channel coding Error probability Random variables Indexes Lossless source coding Slepian-Wolf random access finite blocklength random coding non-asymptotic information theory Gaussian approximation hypothesis testing meta-converse

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On the Rate-Distortion Function for Binary source coding With Side Information

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IEEE TRANSACTIONS ON COMMUNICATIONS 2016年第12期64卷 5203-5216页

作者： Sechelea, Andrei Munteanu, Adrian Cheng, Samuel Deligiannis, Nikos Vrije Univ Brussel Dept Elect & Informat B-1050 Brussels Belgium Tongji Univ Dept Comp Sci & Technol Shanghai 200092 Peoples R China Univ Oklahoma Sch Elect & Comp Engn Tulsa OK 74135 USA

We present an in-depth analysis of the problem of lossy compression of binary sources in the presence of correlated side information, where the correlation is given by a generic binary asymmetric channel and the Hamming distance is the distortion metric. Our analysis is motivated by systematic rate-distortion gains observed when applying asymmetric correlation models in Wyner-Ziv video coding. First, we derive for the first time the rate-distortion function for conventional predictive coding in the binary-asymmetric-correlation-channel scenario. Second, we propose a new bound for the case where the side information is only available at the decoder-Wyner-Ziv coding. We conjecture this bound to be tight. We show that the maximum rate needed to encode as well as the maximum rate-loss of Wyner-Ziv coding relative to predictive coding corresponds to uniform sources and symmetric correlations. Importantly, we show that the upper bound on the rate-loss established by Zamir is not tight and that the maximum value is actually significantly lower. Moreover, we prove that the only binary correlation channel that incurs no rate-loss for Wyner-Ziv coding compared with predictive coding is the Z-channel. Finally, we complement our analysis with new compression performance results obtained with our state-of-the-art Wyner-Ziv video coding system.

关键词： Information theory source coding rate distortion theory video coding

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TEXT-DEPENDENT SPEAKER VERIFICATION USING VECTOR QUANTIZATION source-coding

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IEEE TRANSACTIONS ON ACOUSTICS SPEECH AND SIGNAL PROCESSING 1987年第2期35卷 133-143页

作者： BURTON, DK Entropic Speech Incorporated Washington Research Laboratory Washington DC

Several vector quantization approaches to the problem of text-dependent speaker verification are described. In each of these approaches, a source codebook is designed to represent a particular speaker saying a particular utterance. Later, this same utterance is spoken by a speaker to be verified and is encoded in the source codebook representing the speaker whose identity was claimed. The speaker is accepted if the verification utterance's quantization distortion is less than a prespecified speaker-specific threshold. The best approach achieved a 0.7 percent false acceptance rate and a 0.6 percent false rejection rate on a speaker population comprising 16 admissible speakers and 111 casual imposters. The approaches are described, and detailed experimental results are presented and discussed.

关键词： Vector quantization source coding Speech processing Books Time measurement Linear predictive coding Statistical analysis Training data Probability Decision theory

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Second-Order Asymptotics of Visible Mixed Quantum source coding via Universal Codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2016年第7期62卷 4347-4355页

作者： Leditzky, Felix Datta, Nilanjana Univ Cambridge Stat Lab Ctr Math Sci Cambridge CB3 0WA England

The simplest example of a quantum information source with memory is a mixed source, which emits signals entirely from one of two memoryless quantum sources with given a priori probabilities. Considering a mixed source consisting of a general one-parameter family of memoryless sources, we derive the second-order asymptotic rate for fixed-length visible source coding. Furthermore, we specialize our main result to a mixed source consisting of two memoryless sources. Our results provide the first example of the second-order asymptotics for a quantum information-processing task employing a resource with memory. For the case of a classical mixed source (using a finite alphabet), our results reduce to those obtained by Nomura and Han. To prove the achievability part of our main result, we introduce universal quantum source codes achieving the second-order asymptotic rates. These are obtained by an extension of Hayashi's construction of their classical counterparts.

关键词： Quantum information source coding mixed source second order asymptotics information spectrum

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source coding theorem based on a nonadditive information content

Source coding theorem based on a nonadditive information con...

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International School and Workshop on Non Extensive Thermodynamics and Physical Applications (NEXT 2001)

作者： Yamano, T Univ Cologne Inst Theoret Phys D-50937 Cologne Germany Tokyo Inst Technol Fac Sci Dept Appl Phys Meguro Ku Tokyo 1528551 Japan

A recent attempt to extend Shannon's source coding theorem with a nonadditive information content is briefly reviewed. The information entropy used here is a modified forth of Tsallis entropy (Tsallis entropy divided by the factor E, p,). In addition we refer to some relations which can be worth noting. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： nonextensive statistics information theory source coding

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Joint source coding, routing and power allocation in wireless sensor networks

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IEEE TRANSACTIONS ON COMMUNICATIONS 2008年第6期56卷 886-896页

作者： Yuan, Jun Yu, Wei Univ Toronto Dept Elect & Comp Engn Toronto ON M5S 3G4 Canada

This paper proposes a cross-layer optimization framework for the wireless sensor networks. In a wireless sensor network, each sensor makes a local observation of the underlying physical phenomenon and sends a quantized version of the observation to a central location via wireless links. As the sensor observations are often partial and correlated, the network performance is a complicated and nonseparable function of individual data rates at each sensor. In addition, due to the shared nature of wireless medium, nearby transmissions often interfere with each other. Thus, the traditional "bit-pipe" model for network link capacity no longer holds. This paper deals with the joint optimization of source quantization, routing, and power control in a wireless sensor network. We follow a separate source and channel coding approach and show that the overall network optimization problem can be naturally decomposed into a source coding subproblem at the application layer and a wireless power control subproblem at the physical layer. The interfaces between the layers are precisely the dual optimization variables. In addition, we introduce a novel source coding model at the application layer, which allows the efficient design of practical source quantization schemes at each sensor. Finally, we propose a dual algorithm for the overall network optimization problem. The dual algorithm, when combined with a column-generation method, allows an efficient solution for the overall network optimization problem.

关键词： channel capacity region convex optimization dual decomposition power control rate-distortion region routing sensor networks source coding

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Entropy and source coding for Integer-Dimensional Singular Random Variables

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IEEE TRANSACTIONS ON INFORMATION THEORY 2016年第11期62卷 6124-6154页

作者： Koliander, Guenther Pichler, Georg Riegler, Erwin Hlawatsch, Franz TU Wien Inst Telecommun A-1040 Vienna Austria ETH Dept Informat Technol & Elect Engn CH-8092 Zurich Switzerland

Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension for the practically relevant class of integer-dimensional singular random variables. The proposed entropy definition contains the entropy of discrete random variables and the differential entropy of continuous random variables as special cases. We show that it transforms in a natural manner under Lipschitz functions, and that it is invariant under unitary transformations. We define joint entropy and conditional entropy for integer-dimensional singular random variables, and we show that the proposed entropy conveys useful expressions of the mutual information. As first applications of our entropy definition, we present a result on the minimal expected codeword length of quantized integer-dimensional singular sources and a Shannon lower bound for integer-dimensional singular sources.

关键词： Information entropy rate distortion theory Shannon lower bound singular random variables source coding

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FUSED TREES AND SOME NEW APPROACHES TO source-coding

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IEEE TRANSACTIONS ON INFORMATION THEORY 1988年第3期34卷 417-424页

作者： FITINGOF, B WAKSMAN, Z BEN GURION UNIV NEGEV DEPT MATH BEER SHEVA ISRAEL TEL AVIV UNIV IL-69978 TEL AVIV ISRAEL

The concept of fusion partition for the node set of a tree, and the concept of a fused tree corresponding to it, are discussed. A fused tree requires, in principle, significantly less memory for storage than the original tree yet allows the recovery of the original. Hence, it makes sense to store a tree in a fused form. Furthermore, if labels from an ordered set C are assigned to the branches of the original tree so that a lexographic (alphabetic) order on the set of terminal nodes is induced, a fused tree still enables the execution of direct and inverse enumeration algorithms. A fusion algorithm to produce the completely fused tree for a given tree is presented. Some approaches to data compression problems related to the algorithms given are discussed.< >

关键词： source coding Tree graphs Fusion power generation Graphics Books Data compression Information science Mathematics

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A Delay-Efficient Deep Learning Approach for Lossless Turbo source coding

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2022年第6期71卷 6704-6709页

作者： Manouchehri, Solmaz Haghighat, Javad Eslami, Mohsen Hamouda, Walaa Shiraz Univ Technol Dept Elect Engn Shiraz *** Iran Concordia Univ Elect & Comp Engn Dept Montreal PQ H3G 1M8 Canada

Lossless turbo source coding with decremental/incremental redundancy is a variable-length source coding scheme which employs turbo codes for data compression. Although the scheme offers low compression rates and lends itself to joint source-channel coding, it suffers from a large delay in the encoding phase. The delay is imposed by several tentative encoding-decoding procedures performed at the encoder to search for the minimum compression length. In this work, we apply machine learning to provide a highly accurate estimate of the proper compression length. The encoder starts its search from this estimated length, thus the delay of turbo source coding will decrease considerably. The preliminary results show a four-fold reduction in the encoding delay at the expense of a negligible increase in the compression rate.

关键词： Encoding Iterative decoding Delays Decoding source coding Turbo codes Neurons Data compression delay neural networks turbo code

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