The Gaussian Many-Help-One Distributed Source Coding Problem

Details The Gaussian Many-Help-One Distributed Source Coding Problem The Gaussian Many-Help-One Distributed Source Coding Problem

2008-05-13

arxiv.org/abs/0805.1857v1

Computer Science

Information Theory

Scientific paper

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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