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The Gaussian CEO Problem for Scalar sources With Arbitrary Memory

IEEE TRANSACTIONS ON INFORMATION THEORY 2017年第7期63卷 4286-4297页

作者： Chen, Jie Jiang, Feng Swindlehurst, A. Lee Univ Calif Irvine Ctr Pervas Commun & Comp Irvine CA 92697 USA Univ Calif Irvine Dept Elect Engn & Comp Sci Irvine CA 92697 USA Nokia Networks Arlington Hts Arlington Hts IL 60004 USA Intel Corp Santa Clara Santa Clara CA 95054 USA

In this paper, we consider the achievable sum-rate/distortion tradeoff for the Gaussian central estimation officer (CEO) problem with a scalar source having arbitrary memory. We describe how the arbitrary memory problem can be fully characterized by using known results for the vector CEO problem, and then we formulate the variational problem of minimizing the sum-rate subject to a distortion constraint. To solve the problem, we extend the conventional Lagrange method and show that if the solution exists, it should consist of a zero part and a non-zero part, where the non-zero part is determined by solving a set of Euler equations. By calculating the second variation of the min-sum-rate problem, a sufficient condition is also found that can be used to determine if the necessary solution results in the minimal sum rate. The special case of two terminals is examined in detail, and it is shown that an analytical solution is possible in this case. Analysis and discussion with examples are provided to illustrate the theoretical results. The general solution obtained in this paper is shown to be compatible with the previous results for cases such as the problem of rate evaluation for sources without memory.

关键词： multiterminal source coding CEO problem decentralized estimation Gaussian sources with memory variational calculus

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Distributed Rate-Distortion With Common Components

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IEEE TRANSACTIONS ON INFORMATION THEORY 2011年第7期57卷 4035-4057页

作者： Wagner, Aaron B. Kelly, Benjamin G. Altug, Yuecel Cornell Univ Sch Elect & Comp Engn Ithaca NY 14853 USA

We describe a scheme for rate-distortion with distributed encoding in which the sources to be compressed contain a common component. We show that this scheme is optimal in some situations and that it strictly improves upon existing schemes, which do not make full use of common components. This establishes that independent quantization followed by independent binning is not optimal for the two-encoder problem with a distortion constraint on one source. We also show that independent quantization and binning is suboptimal for the three-encoder problem in which the goal is to reproduce one of the sources losslessly. This provides a counterexample that is fundamentally different from one provided earlier by Korner and Marton. The proofs rely on the binary analogue of the entropy power inequality and the existence of a rate loss for the binary symmetric Wyner-Ziv problem.

关键词： Common randomness entropy power inequality lossy compression multiterminal source coding one-helper problem rate region rate-distortion

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Low-density parity-check matrices for coding of correlated sources

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IEEE TRANSACTIONS ON INFORMATION THEORY 2005年第10期51卷 3645-3654页

作者： Muramatsu, J Uyematsu, T Wadayama, T NTT Corp NTT Commun Sci Labs Kyoto 6190237 Japan Tokyo Inst Technol Meguro Ku Tokyo 1528552 Japan Nagoya Inst Technol Showa Ku Nagoya Aichi 4668555 Japan

Linear codes for a coding problem of correlated sources are considered. It is proved that we can construct codes by using low-density parity-check (LDPC) matrices with maximum-likelihood (or typical set) decoding. As applications of the above coding problem, a construction of codes is presented for multiple-access channel with correlated additive noises and a coding theorem of parity-check codes for general channels is proved.

关键词： linear codes low-density parity-check (LDPC) matrix multiterminal source coding multiterminal channel coding multiple-access channel with correlated additive noise Slepian-Wolf source coding

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Network information flow

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IEEE TRANSACTIONS ON INFORMATION THEORY 2000年第4期46卷 1204-1216页

作者： Ahlswede, R Cai, N Li, SYR Yeung, RW Univ Bielefeld Fak Math D-33501 Bielefeld Germany Chinese Univ Hong Kong Dept Informat Engn Hong Kong Hong Kong Peoples R China

We introduce a new class of problems called network information flow which is inspired by computer network applications. Consider a point-to-point communication network on which a number of information sources are to be mulitcast to certain sets of destinations. We assume that the information sources are mutually independent. The problem is to characterize the admissible coding rate region. This model subsumes all previously studied models along the same line. In this paper, we study the problem with one information source, and we have obtained a simple characterization of the admissible coding rate region. Our result can be regarded as the Max-flow Min-cut Theorem for network information flow. Contrary to one's intuition, our work reveals that it is in general not optimal to regard the information to be multicast as a "fluid'' which can simply be routed or replicated. Rather, by employing coding at the nodes, which we refer to as network coding, bandwidth can in general be saved. This finding may have significant impact on future design of switching systems.

关键词： diversity coding multicast network coding switching multiterminal source coding

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Network information flow with correlated sources

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IEEE TRANSACTIONS ON INFORMATION THEORY 2006年第1期52卷 155-170页

作者： Barros, J Servetto, SD Tech Univ Munich Inst Commun Engn D-8000 Munich Germany Cornell Univ Sch Elect & Comp Engn Ithaca NY 14853 USA

Consider the following network communication setup, originating in a sensor networking application we refer to as the "sensor reachback" problem. We have a directed graph G = (V, E), where V = {v(0)v(1)...v(n)} and E subset of V x V. If (v(i), v(j)) is an element of E, then node i can send messages to node j over a discrete memoryless channel (DMC) (X-ij, p(ij)(y vertical bar X), Y-ij), of capacity C-ij. The channels are independent. Each node v(i) gets to observe a source of information U-i(i = 0...M), with joint distribution p(U0U1...U-M). Our goal is to solve an incast problem in G: nodes exchange messages with their neighbors, and after a finite number of communication rounds, one of the M + 1 nodes (v(0) by convention) must have received enough information to reproduce the entire field of observations (U0U1...U-M), with arbitrarily small probability of error. In this paper, we prove that such perfect reconstruction is possible if and only if H(U-S vertical bar U-Sc) < Sigma(i is an element of S,j is an element of Sc) C-ij for all S subset of {0...M}, S not equal circle divide, 0 is an element of S-c. Our main finding is that in this setup;a general source/channel separation theorem holds, and that Shannon information behaves as a classical network flow, identical in nature to the flow of water in pipes. At first glance, it might seem surprising that separation holds in a fairly general network situation like the one we study. A. closer look, however, reveals that the reason for this is that our model allows only for independent point-to-point channels between pairs of nodes, and not multiple-access and/or broadcast channels, for which separation is well known not to hold. This "information as flow" view provides an algorithmic interpretation for our results, among which perhaps the most important one is the optimality of implementing codes using a layered protocol stack.

关键词： communication networks correlated sources directed graphs multiterminal source coding network algorithhms network analysis network architecture network capacity network coding network design network flow network protocols networks routing sensor networks

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On symmetrical multilevel diversity coding

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IEEE TRANSACTIONS ON INFORMATION THEORY 1999年第2期45卷 609-621页

作者： Yeung, RW Zhang, Z Chinese Univ Hong Kong Dept Informat Engn Hong Kong NT Peoples R China Univ So Calif Dept Elect Engn Syst Inst Commun Sci Los Angeles CA 90089 USA

Symmetrical multilevel diversity coding with independent data streams has recently been studied by Roche et al., and the admissible coding rate region was determined for the case of three levels. In particular, it was shown that coding by superposition is optimal, which means that optimality can be achieved by very simple coding. However, it is very difficult to generalize their proof to an arbitrary number of levels, In this paper, we use a new approach to study this problem, and we show that coding by superposition is optimal for symmetrical multilevel diversity coding in general, We also discuss how our result can be applied when the source consists of correlated data streams. The techniques we use are new in multiuser information theory, and our work sheds some light on the standing problem of characterizing those multilevel diversity coding systems for which coding by superposition is optimal.

关键词： diversity coding multilevel systems multiterminal source coding multiuser information theory

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MULTILEVEL DIVERSITY coding WITH DISTORTION

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IEEE TRANSACTIONS ON INFORMATION THEORY 1995年第2期41卷 412-422页

作者： YEUNG, RW Chinese Univ of Hong Kong Shatin Hong Kong

In a Diversity coding System, an information source is encoded by a number of encoders. There are a number of decoders, each of which can access a certain subset of the encoders. In this paper, we study a diversity coding problem in which there are two levels of decoders. The reconstructions of the source by decoders within the same level are identical, and are subject to the same distortion criterion. Our results imply a principle of superposition when the source consists of two independent data streams. Practical codes achieving zero error can easily be constructed for this special case. A class of open problems on this topic is also suggested.

关键词： multiterminal source coding DIVERSITY coding FAULT TOLERANCE PRINCIPLE OF SUPERPOSITION

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The CEO Problem With rth Power of Difference and Logarithmic Distortions

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IEEE TRANSACTIONS ON INFORMATION THEORY 2021年第6期67卷 3873-3891页

作者： Seo, Daewon Varshney, Lav R. Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA Univ Wisconsin Madison Dept Elect & Comp Engn Madison WI 53706 USA Univ Illinois Coordinated Sci Lab Urbana IL 61801 USA

The CEO problem has received much attention since first introduced by Berger et al., but there are limited results on non-Gaussian models with non-quadratic distortion measures. In this work, we extend the quadratic Gaussian CEO problem to two non-Gaussian settings with general rth power of difference distortion. Assuming an identical observation channel across agents, we study the asymptotics of distortion decay as the number of agents and sum-rate, Rsum, grow without bound, while individual rates vanish. The first setting is a regular source-observation model with rth power of difference distortion, which subsumes the quadratic Gaussian CEO problem, and we establish that the distortion decays at O(R-sum(-r/2)) when r >= 2. We use sample median estimation after the Berger-Tung scheme for achievability. The other setting is a non-regular sourceobservation model, including uniform additive noise models, with rth power of difference distortion for which estimation-theoretic regularity conditions do not hold. The distortion decay O(R- rsum) when r >= 1 is obtained for the non-regular model by midrange estimator following the Berger-Tung scheme. We also provide converses based on the Shannon lower bound for the regular model and the Chazan-Zakai-Ziv bound for the non-regular model, respectively. Lastly, we provide a sufficient condition for the regular model, under which quadratic and logarithmic distortions are asymptotically equivalent by an entropy power relationship as the number of agents grows. This proof relies on the Bernstein-von Mises theorem.

关键词： CEO problem multiterminal source coding median estimator midrange estimator Shannon lower bound Chazan-Zakai-Ziv bound

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Sequential coding of correlated sources

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IEEE TRANSACTIONS ON INFORMATION THEORY 2000年第1期46卷 236-246页

作者： Viswanathan, H Berger, T Cornell Univ Sch Elect Engn Ithaca NY 14850 USA

We study a generalization of the successive refinement coding problem called the sequential coding of correlated sources. In successive refinement source coding one first describes the given source using a few bits of information, and then subsequently improves the description of the same source when more information is supplied. Sequential coding differs from successive refinement in that the second-stage encoding involves describing a correlated source as opposed to improving the description of the same source. We introduce the notion of a coupled fidelity criterion to quantify perceived distortion in certain applications of sequential coding. We characterize the achievable rate region far this source coding problem and show that the rate region reduces to the successive refinement rate region when the two sources are the same. Then we consider the specific case of a pair of correlated Gaussian sources as an example. We give an explicit characterization that reveals an interesting generalization of a property of successive refinement of a single Gaussian source.

关键词： Gaussian source coding multiterminal source coding perceptual distortion sequential coding successive refinement

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Vector Gaussian CEO Problem Under Logarithmic Loss and Applications

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IEEE TRANSACTIONS ON INFORMATION THEORY 2020年第7期66卷 4183-4202页

作者： Ugur, Yigit Aguerri, Inaki Estella Zaidi, Abdellatif Univ Paris Est Lab Informat Gaspard Monge F-77454 Champs Sur Marne France Huawei Technol Paris Res Ctr Math & Algorithm Sci Lab F-92100 Boulogne France Telephon Innovac Alpha Barcelona 08019 Spain

In this paper, we study the vector Gaussian Chief Executive Officer (CEO) problem under logarithmic loss distortion measure. Specifically, K >= 2 agents observe independently corrupted Gaussian noisy versions of a remote vector Gaussian source, and communicate independently with a decoder or CEO over rate-constrained noise-free links. The CEO also has its own Gaussian noisy observation of the source and wants to reconstruct the remote source to within some prescribed distortion level where the incurred distortion is measured under the logarithmic loss penalty criterion. We find an explicit characterization of the rate-distortion region of this model. The result can be seen as the counterpart to the vector Gaussian setting of that by Courtade-Weissman which provides the rate-distortion region of the model in the discrete memoryless setting. For the proof of this result, we obtain an outer bound by means of a technique that relies on the de Bruijn identity and the properties of Fisher information. The approach is similar to Ekrem-Ulukus outer bounding technique for the vector Gaussian CEO problem under quadratic distortion measure, for which it was there found generally non-tight;but it is shown here to yield a complete characterization of the region for the case of logarithmic loss measure. Also, we show that Gaussian test channels with time-sharing exhaust the Berger-Tung inner bound, which is optimal. Furthermore, application of our results allows us to find the complete solutions of two related problems: a quadratic vector Gaussian CEO problem with determinant constraint and the vector Gaussian distributed Information Bottleneck problem. Finally, we develop Blahut-Arimoto type algorithms that allow to compute numerically the regions provided in this paper, for both discrete and Gaussian models. With the known relevance of the logarithmic loss fidelity measure in the context of learning and prediction, the proposed algorithms may find usefulness in a variety of app

关键词： Loss measurement Distortion Rate-distortion Distortion measurement source coding Noise measurement Decoding multiterminal source coding distributed source coding CEO problem rate-distortion region Berger-Tung inner bound logarithmic loss information bottleneck Blahut-Arimoto algorithm

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