Rate Distortion Function for a Class of Relative Entropy Sources

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. I. INTRODUCTION This paper is concerned with lossy data compression for a class of sources defined on the space of probability distributions on general alphabet spaces. In the classical rate distortion formulation with the fidelity decoding criterion, Shannon has shown that minimization of mutual information between finite alphabet source and reproduction sequences subject to fidelity criterion over the reproduction kernel has an operational meaning. Hence, it gives the minimum amount of information of representing a source symbol by a reproduction symbol with a pre-specified fidelity or distortion criterion.