Indirect Rate Distortion Functions with f-Separable Distortion Criterion
Résumé
We consider a remote source coding problem subject to a distortion fidelity. Contrary to the use of the classical separable distortion criterion, herein we consider the more general, f-separable distortion measure and study its implications on the characterization of the minimum achievable rates (also called fseparable 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 f-separable distortion. Our main result is a single-letter characterization of the fseparable 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 f-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.
Domaines
Informatique [cs]
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