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Vector Gaussian CEO Problem Under Logarithmic Loss and Applications

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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The Lossy Common Information of Correlated sources

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IEEE TRANSACTIONS ON INFORMATION THEORY 2014年第6期60卷 3238-3253页

作者： Viswanatha, Kumar B. Akyol, Emrah Rose, Kenneth Univ Calif Santa Barbara Dept Elect & Comp Engn Santa Barbara CA 93106 USA Univ So Calif Dept Elect Engn Los Angeles CA 90089 USA

The two most prevalent notions of common information (CI) are due to Wyner and Gacs-Korner and both the notions can be stated as two different characteristic points in the lossless Gray-Wyner region. Although the information theoretic characterizations for these two CI quantities can be easily evaluated for random variables with infinite entropy (e. g., continuous random variables), their operational significance is applicable only to the lossless framework. The primary objective of this paper is to generalize these two CI notions to the lossy Gray-Wyner network, which hence extends the theoretical foundation to general sources and distortion measures. We begin by deriving a single letter characterization for the lossy generalization of Wyner's CI, defined as the minimum rate on the shared branch of the Gray-Wyner network, maintaining minimum sum transmit rate when the two decoders reconstruct the sources subject to individual distortion constraints. To demonstrate its use, we compute the CI of bivariate Gaussian random variables for the entire regime of distortions. We then similarly generalize Gacs and Korner's definition to the lossy framework. The latter half of this paper focuses on studying the tradeoff between the total transmit rate and receive rate in the Gray-Wyner network. We show that this tradeoff yields a contour of points on the surface of the Gray-Wyner region, which passes through both the Wyner and Gacs-Korner operating points, and thereby provides a unified framework to understand the different notions of CI. We further show that this tradeoff generalizes the two notions of CI to the excess sum transmit rate and receive rate regimes, respectively.

关键词： Common information Gray-Wyner network multiterminal source coding

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Symmetrical multilevel diversity coding

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IEEE TRANSACTIONS ON INFORMATION THEORY 1997年第3期43卷 1059-1064页

作者： Roche, JR Yeung, RW Hau, KP CHINESE UNIV HONG KONG DEPT INFORMAT ENGN SHATIN NT HONG KONG

Multilevel diversity coding was introduced in recent work by Roche and Yeung. In a multilevel diversity coding system, an information source is encoded by a number of encoders. There is a set of decoders, partitioned into multiple levels, with each decoder having access to a certain subset of the encoders. The reconstructions of the source by decoders within the same level are identical and are subject to the same distortion criterion. Inspired by applications in computer communication and fault-tolerant data retrieval, we study a multilevel diversity coding problem with three levels for which the connectivity between the encoders and decoders is symmetrical. We obtain a single-letter characterization of the coding rate region and show that coding by superposition is optimal for this problem. Generalizing to a symmetrical problem with an arbitrary number of levels, we derive a tight lower bound on the coding rate sum.

关键词： coding by superposition diversity coding fault-tolerance multiterminal source coding

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Side information aware coding strategies for sensor networks

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS 2004年第6期22卷 966-976页

作者： Draper, SC Wornell, GW Univ Calif Berkeley Dept Elect & Comp Engn Berkeley CA 94720 USA MIT Dept Elect Engn & Comp Sci Cambridge MA 02139 USA

We develop coding strategies for estimation under communication constraints in tree-structured sensor networks. The strategies have a modular and decentralized architecture. This promotes the flexibility, robustness, and scalability that wireless sensor networks need to operate in uncertain, changing, and resource-constrained environments. The strategies are based on a generalization of Wyner-Ziv source coding with decoder side information. We develop solutions for general trees, and illustrate our results in serial (pipeline) and parallel (hub-and-spoke) networks. Additionally, the strategies can be applied to other network information theory problems. They have a successive coding structure that gives an inherently less complex way to attain a number of prior results, as well as some novel results, for the Chief Executive Officer problem, multiterminal source coding, and certain classes of relay channels.

关键词： Chief Executive Officer (CEO) problems data fusion distributed defection distributed estimation multiterminal source coding rate distortion theory relay channels sensor networks side information Wyner-Ziv coding

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The Non-Regular CEO Problem

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IEEE TRANSACTIONS ON INFORMATION THEORY 2015年第5期61卷 2764-2775页

作者： Vempaty, Aditya Varshney, Lav R. Syracuse Univ Dept Elect Engn & Comp Sci Syracuse NY 13244 USA Univ Illinois Coordinated Sci Lab Champaign IL 61820 USA Univ Illinois Dept Elect & Comp Engn Champaign IL 61820 USA

We consider the CEO problem for non-regular source distributions (such as uniform or truncated Gaussian). A group of agents observe independently corrupted versions of data and transmit coded versions over rate-limited links to a CEO. The CEO then estimates the underlying data based on the received coded observations. Agents are not allowed to convene before transmitting their observations. This formulation is motivated by the practical problem of a firm's CEO estimating (non-regular) beliefs about a sequence of events, before acting on them. Agents' observations are modeled as jointly distributed with the underlying data through a given conditional probability density function. We study the asymptotic behavior of the minimum achievable mean squared error distortion at the CEO in the limit when the number of agents L and the sum rate R tend to infinity. We establish a 1/R-2 convergence of the distortion, an intermediate regime of performance between the exponential behavior in discrete CEO problems [Berger, Zhang, and Viswanathan (1996)], and the 1/R behavior in Gaussian CEO problems [Viswanathan and Berger (1997)]. Achievability is proved by a layered architecture with scalar quantization, distributed entropy coding, and midrange estimation. The converse is proved using the Bayesian Chazan-Zakai-Ziv bound.

关键词： multiterminal source coding mean-square error midrange estimator Chazan-Zakai-Ziv bound

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Malleable coding for Updatable Cloud Caching

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IEEE TRANSACTIONS ON COMMUNICATIONS 2016年第12期64卷 4946-4955页

作者： Varshney, Lav R. Kusuma, Julius Goyal, Vivek K. Univ Illinois Coordinated Sci Lab Urbana IL 61801 USA Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA Schlumberger Doll Res Ctr Telemetry Res Cambridge MA 02139 USA Boston Univ Dept Elect & Comp Engn Boston MA 02215 USA

In software-as-a-service applications provisioned through cloud computing, locally cached data are often modified with updates from new versions. In some cases, with each edit, one may want to preserve both the original and new versions. In this paper, we focus on cases in which only the latest version must be preserved. Furthermore, it is desirable for the data to not only be compressed but to also be easily modified during updates, since representing information and modifying the representation both incur cost. We examine whether it is possible to have both compression efficiency and ease of alteration, in order to promote codeword reuse. In other words, we study the feasibility of a malleable and efficient coding scheme. The tradeoff between compression efficiency and malleability cost-the difficulty of synchronizing compressed versions-is measured as the length of a reused prefix portion. The region of achievable rates and malleability is found. Drawing from prior work on common information problems, we show that efficient data compression may not be the best engineering design principle when storing software-as-a-service data. In the general case, goals of efficiency and malleability are fundamentally in conflict.

关键词： Caching cloud computing common information concurrency control data compression multiterminal source coding

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On the whiteness of high-resolution quantization errors

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IEEE TRANSACTIONS ON INFORMATION THEORY 2001年第5期47卷 2029-2038页

作者： Viswanathan, H Zamir, R Bell Labs Lucent Technol Murray Hill NJ 07924 USA Tel Aviv Univ Dept Elect Engn Syst IL-69978 Tel Aviv Israel

A common belief in quantization theory says that the quantization noise process resulting from uniform sc alar quantization of a correlated discrete-time process tends to be white in the limit of small distortion ("high resolution"). A rule of thumb for this property to hold is that the source samples have a "smooth" joint distribution. We give a precise statement of this property, and generalize it to nonuniform quantization and to vector quantization, We show that the quantization errors resulting from independent quantizations of dependent real random variables become asymptotically uncorrelated (although not necessarily statistically independent) if the joint Fisher information (FI) under translation of the two variables is finite and the quantization cells shrink uniformly as the distortion tends to zero.

关键词： asymptotic whiteness Fisher information (FI) high resolution multiterminal source coding quantization noise

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A semi-continuous version of the Berger-Yeung problem

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IEEE TRANSACTIONS ON INFORMATION THEORY 1999年第5期45卷 1520-1526页

作者： Berger, T Zamir, R Cornell Univ Sch Elect Engn Ithaca NY 14853 USA Tel Aviv Univ Dept Elect Syst Engn IL-69978 Tel Aviv Israel

We present a continuous dual of multiterminal source encoding with one distortion criterion (the "Berger-Yeung problem"), A continuous source X is encoded with "high resolution" (D-x --> O), with the aid of a "helper," i.e., a correlated discrete or continuous source II, that is encoded separately subject to some arbitrary distortion criterion D-y, We find the asymptotic form of the set of achievable coding rates R(D-x, D-y) of the Sand Y-encoders as D-x --> 0. Two extreme cases of our result provide high-resolution interpretations to the classical work of Wyner, Ahlswede, Korner, and Ziv on source coding with side information.

关键词： Berger-Yeung problem high resolution multiterminal source coding Shannon lower bound side information Wyner-Ziv problem

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The rate-distortion function for the quadratic gaussian CEO problem

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IEEE TRANSACTIONS ON INFORMATION THEORY 1998年第3期44卷 1057-1070页

作者： Oohama, Y Kyushu Univ Grad Sch Informat Sci & Elect Engn Higashi Ku Fukuoka 812 Japan

A new multiterminal source coding problem called the CEO problem was presented and investigated by Berger, Zhang, and Viswanathan, Recently, Viswanathan and Berger have investigated an extension of the CEO problem to Gaussian sources and call it the quadratic Gaussian CEO problem. They considered this problem from a statistical viewpoint, deriving some interesting results. In this paper, we consider the quadratic Gaussian CEO problem from a standpoint of multiterminal rate-distortion theory. We regard the CEO problem as a certain multiterminal remote source coding problem with infinitely many separate encoders whose observations are conditionally independent if the remote source is given. This viewpoint leads us to a complete solution to the problem. We determine the tradeoff between the total amount of rate and squared distortion, deriving an explicit formula of the rate-distortion function. The derived function has the form of a sum of two nonnegative functions. One is a classical rate-distortion function for single Gaussian source and the other is a new rate-distortion function which dominates the performance of the system for a relatively small distortion. It follows immediately from our result that the conjecture of Viswanathan and Berger on the asymptotic behavior of minimum squared distortion for large rates is true.

关键词： Gaussian many separate encoders multiterminal rate-distortion theory multiterminal source coding

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Zero-effor network coding for acyclic networks

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IEEE TRANSACTIONS ON INFORMATION THEORY 2003年第12期49卷 3129-3139页

作者： Song, LH Yeung, RW Univ Utah Dept Elect Engn Salt Lake City UT 84112 USA Chinese Univ Hong Kong Dept Informat Engn Hong Kong Hong Kong Peoples R China

Consider transmitting a set of information sources through a communication network that consists of a number of nodes. Between certain pair of nodes, there exist communication channels on which information can be transmitted. At a node, one or more information sources may be generated, and each of them is multicast to a set of destination nodes on the network. In this paper, we study the problem of under what conditions a set of mutually independent information sources can be faithfully transmitted through a communication network, for which the connectivity among the nodes and the multicast requirements of the source information are arbitrary except that the connectivity does not form directed cycles. We obtain inner and outer bounds on the zero-error admissible coding rate region in term of the regions Gamma(N)* and (Γ) over bar (N)* which are fundamental regions in the entropy space defined by Yeung. The results in this paper can be regarded as zero-error network coding theorems for acyclic communication networks.

关键词： acyclic network multicast multiterminal source coding network coding zero error

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