Worst-Case Source for Distributed Compression with Quadratic Distortion

TL;DR

This paper demonstrates that for the distributed source coding problem with quadratic distortion, the Gaussian source distribution demands the highest rates among all sources with the same covariance, establishing a worst-case scenario.

Contribution

It identifies the Gaussian source as the worst-case distribution for rate requirements in distributed quadratic source coding with fixed covariance.

Findings

Gaussian source requires the highest rates for given covariance and distortion constraints.

The result establishes a worst-case source distribution in distributed compression.

The analysis applies to the k-encoder source coding problem with quadratic distortion.

Abstract

We consider the k-encoder source coding problem with a quadratic distortion measure. We show that among all source distributions with a given covariance matrix K, the jointly Gaussian source requires the highest rates in order to meet a given set of distortion constraints.