Indirect Rate Distortion Functions with f-Separable Distortion Criterion
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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, f-separable distortion measure and study its implications on the characterization of the minimum achievable rates (also called f-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 f-separable distortion. Our main result is a single-letter characterization of the f-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 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.
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