Distributed Remote Vector Gaussian Source Coding with Covariance Distortion Constraints

TL;DR

This paper investigates the optimal rate-distortion trade-off in distributed remote Gaussian source coding with covariance constraints, providing bounds, exact solutions in special cases, and generalizations of prior results.

Contribution

It derives new bounds and exact solutions for the Gaussian case, extending previous work and unifying different distortion measures under a common framework.

Findings

Derived lower and upper bounds on the rate-distortion function.

Identified cases where the rate-distortion function can be exactly computed.

Unified previous results and extended them to broader scenarios.

Abstract

In this paper, we consider a distributed remote source coding problem, where a sequence of observations of source vectors is available at the encoder. The problem is to specify the optimal rate for encoding the observations subject to a covariance matrix distortion constraint and in the presence of side information at the decoder. For this problem, we derive lower and upper bounds on the rate-distortion function (RDF) for the Gaussian case, which in general do not coincide. We then provide some cases, where the RDF can be derived exactly. We also show that previous results on specific instances of this problem can be generalized using our results. We finally show that if the distortion measure is the mean squared error, or if it is replaced by a certain mutual information constraint, the optimal rate can be derived from our main result.