%0 Journal Article
%T The Gaussian Many-Help-One Distributed Source Coding Problem
%A Saurabha Tavildar
%A Pramod Viswanath
%A Aaron B. Wagner
%J Mathematics
%D 2008
%I arXiv
%X 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.
%U http://arxiv.org/abs/0805.1857v1