On Distributed Lossy Coding of Symmetrically Correlated Gaussian Sources

TL;DR

This paper derives a lower bound on the rate-distortion function for distributed lossy coding of Gaussian sources with symmetric noise, matching known bounds in some cases and analyzing the asymptotic gap as the number of encoders grows.

Contribution

It provides an explicit lower bound on the rate-distortion function for a class of Gaussian sources, extending understanding of distributed lossy compression limits.

Findings

Lower bound matches Berger-Tung upper bound for some distortion levels.

Explicit characterization of the asymptotic gap as the number of encoders increases.

Analysis of the rate-distortion trade-off in symmetric Gaussian source networks.

Abstract

A distributed lossy compression network with $L$ encoders and a decoder is considered. Each encoder observes a source and sends a compressed version to the decoder. The decoder produces a joint reconstruction of target signals with the mean squared error distortion below a given threshold. It is assumed that the observed sources can be expressed as the sum of target signals and corruptive noises which are independently generated from two symmetric multivariate Gaussian distributions. The minimum compression rate of this network versus the distortion threshold is referred to as the rate-distortion function, for which an explicit lower bound is established by solving a minimization problem. Our lower bound matches the well-known Berger-Tung upper bound for some values of the distortion threshold. The asymptotic gap between the upper and lower bounds is characterized in the large $L$ limit.