Rate Distortion Function for a Class of Relative Entropy Sources

TL;DR

This paper develops a robust rate distortion framework for sources with uncertainty characterized by relative entropy constraints, providing explicit minimax solutions and extending classical results to uncertain source classes.

Contribution

It introduces a minimax approach to rate distortion for sources with distributional uncertainty, generalizing classical solutions and explicitly computing strategies.

Findings

Explicit minimax solutions for robust source coding

Extension of rate distortion theorem to uncertain sources

Closed-form strategies for discrete memoryless sources

Abstract

This paper deals with rate distortion or source coding with fidelity criterion, in measure spaces, for a class of source distributions. The class of source distributions is described by a relative entropy constraint set between the true and a nominal distribution. The rate distortion problem for the class is thus formulated and solved using minimax strategies, which result in robust source coding with fidelity criterion. It is shown that minimax and maxmin strategies can be computed explicitly, and they are generalizations of the classical solution. Finally, for discrete memoryless uncertain sources, the rate distortion theorem is stated for the class omitting the derivations while the converse is derived.