Network Compression: Worst-Case Analysis

TL;DR

This paper analyzes the worst-case scenarios in network compression, showing Gaussian sources and noise are hardest to compress or communicate over, with constructive schemes applicable beyond Gaussian cases based on covariance.

Contribution

It establishes that Gaussian sources and noise are the least compressible and communicable in worst-case scenarios, providing constructive methods for non-Gaussian cases with the same covariance.

Findings

Gaussian sources are least compressible among all sources with the same correlation.

Gaussian noise admits the smallest achievable distortion set over additive-noise networks.

Constructive schemes for Gaussian cases extend to non-Gaussian cases with identical covariance.

Abstract

We study the problem of communicating a distributed correlated memoryless source over a memoryless network, from source nodes to destination nodes, under quadratic distortion constraints. We establish the following two complementary results: (a) for an arbitrary memoryless network, among all distributed memoryless sources of a given correlation, Gaussian sources are least compressible, that is, they admit the smallest set of achievable distortion tuples, and (b) for any memoryless source to be communicated over a memoryless additive-noise network, among all noise processes of a given correlation, Gaussian noise admits the smallest achievable set of distortion tuples. We establish these results constructively by showing how schemes for the corresponding Gaussian problems can be applied to achieve similar performance for (source or noise) distributions that are not necessarily Gaussian but have the same covariance.