Indirect Rate Distortion Functions with $f$-Separable Distortion Criterion
| Autor: | Stavrou, Photios A., Shkel, Yanina, Kountouris, Marios |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 6 pages, 2 figures, accepted for publication to the proceedings of ISIT 2023 |
| Databáze: | arXiv |
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