Indirect Rate Distortion Functions with -Separable Distortion Criterion
arXiv:2305.10549
Abstract
We consider a remote source coding problem subject to a {distortion function}. Contrary to the use of the classical separable distortion criterion, herein we consider the more general, -separable distortion measure and study its implications on the characterization of the minimum achievable rates (also called -separable indirect rate distortion function (iRDF)) under both excess and average distortion constraints. First, we provide a single-letter characterization of the optimal rates subject to an excess distortion using properties of the -separable distortion. Our main result is a single-letter characterization of the -separable iRDF subject to an average distortion constraint. As a consequence of the previous results, we also show a series of equalities that hold using either indirect or classical RDF under -separable excess or average distortions. We corroborate our results with two application examples in which new closed-form solutions are derived, and based on these, we also recover known special cases.
6 pages, 2 figures, accepted for publication to the proceedings of ISIT 2023