Indirect Rate Distortion Functions with $f$-Separable Distortion Criterion
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.
Cite
@article{arxiv.2305.10549,
title = {Indirect Rate Distortion Functions with $f$-Separable Distortion Criterion},
author = {Photios A. Stavrou and Yanina Shkel and Marios Kountouris},
journal= {arXiv preprint arXiv:2305.10549},
year = {2023}
}
Comments
6 pages, 2 figures, accepted for publication to the proceedings of ISIT 2023