标题： 高斯多助一分布式信源编码问题 显示英文标题

标题： The Gaussian Many-Help-One Distributed Source Coding Problem

摘要： N个不同终端观察到联合高斯无记忆信源。 目标是以高效的方式以分布式方式对观测值进行编码，以便在解码器端根据二次保真度准则重建任意一个观测值，例如第一个观测值。 我们的主要结果是当信源的协方差矩阵满足“树结构”条件时，对率失真区域的精确表征。 在这种情况下，一种自然的模拟-数字分离方案最优地权衡了分布式量化率元组和重建失真：每个编码器由点对点高斯矢量量化器和Slepian-Wolf分组编码器组成。 我们还提供了一个部分逆定理，表明树结构条件是基本的。 显示英文摘要

摘要： 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.