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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 Â¿tree-structureÂ¿ 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.
Date of Publication: Jan. 2010