The Gaussian Many-Help-One Distributed Source Coding Problem

Jointly Gaussian memoryless sources are observed at N distinct terminals. The goal is to efficiently encode the observations in a distributed fashion so as to enable reconstruction of any one of the observations, say the first one, at the decoder subject to a quadratic fidelity criterion. Our main r...

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Bibliographic Details
Published in:	IEEE transactions on information theory Vol. 56; no. 1; pp. 564 - 581
Main Authors:	Tavildar, S., Viswanath, P., Wagner, A.B.
Format:	Journal Article
Language:	English
Published:	New York, NY IEEE 01.01.2010 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Applied sciences Coders Codes Coding, codes Covariance matrix Decoding Distortion Encoders Engineering profession Entropy power inequality Exact sciences and technology Gaussian Gaussian distribution Gaussian processes Gaussian sources Information processing Information theory Information, signal and communications theory many-help-one problem Mathematical analysis Matrix network source coding Normal distribution Optimization Rate-distortion Reconstruction Sampling, quantization Signal and communications theory Source coding Statistics Telecommunications and information theory Terminals tree sources Vector quantization Source coding Vector quantization tree sources Distributed source signal Rate distortion theory Entropy Tree structure Decoding Covariance matrix rate distortion network source coding many-help-one problem Signal quantization Gaussian sources Memoryless source Entropy power inequality
ISSN:	0018-9448, 1557-9654
Online Access:	Get full text
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Summary:	Jointly Gaussian memoryless sources are observed at N distinct terminals. The goal is to efficiently encode the observations in a distributed fashion so as to enable reconstruction of any one of the observations, say the first one, at the decoder subject to a quadratic fidelity criterion. Our main result is a precise characterization of the rate-distortion region when the covariance matrix of the sources satisfies a ¿tree-structure¿ condition. In this situation, a natural analog-digital separation scheme optimally trades off the distributed quantization rate tuples and the distortion in the reconstruction: each encoder consists of a point-to-point Gaussian vector quantizer followed by a Slepian-Wolf binning encoder. We also provide a partial converse that suggests that the tree-structure condition is fundamental.
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ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2009.2034791