Source Coding in Networks with Covariance Distortion Constraints

TL;DR

This paper derives an explicit rate-distortion function for a Gaussian vector source coding problem with covariance constraints, unifying several existing problems and applying results to optimize network denoising performance.

Contribution

It introduces a new covariance matrix distortion measure and provides a closed-form rate-distortion function, unifying and extending prior Gaussian source coding results.

Findings

Derived an explicit formula for the rate-distortion function under covariance constraints

Unified existing Gaussian Wyner-Ziv problems as special cases

Applied the theory to optimize SNR in network denoising scenarios

Abstract

We consider a source coding problem with a network scenario in mind, and formulate it as a remote vector Gaussian Wyner-Ziv problem under covariance matrix distortions. We define a notion of minimum for two positive-definite matrices based on which we derive an explicit formula for the rate-distortion function (RDF). We then study the special cases and applications of this result. We show that two well-studied source coding problems, i.e. remote vector Gaussian Wyner-Ziv problems with mean-squared error and mutual information constraints are in fact special cases of our results. Finally, we apply our results to a joint source coding and denoising problem. We consider a network with a centralized topology and a given weighted sum-rate constraint, where the received signals at the center are to be fused to maximize the output SNR while enforcing no linear distortion. We show that one can design the distortion matrices at the nodes in order to maximize the output SNR at the fusion center. We thereby bridge between denoising and source coding within this setup.