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Exponential Strong Converse for Successive Refinement with Causal Decoder Side Information †
We consider the k-user successive refinement problem with causal decoder side information and derive an exponential strong converse theorem. The rate-distortion region for the problem can be derived as a straightforward extension of the two-user case by Maor and Merhav (2008). We show that for any r...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2019
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514900/ https://www.ncbi.nlm.nih.gov/pubmed/33267124 http://dx.doi.org/10.3390/e21040410 |
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author | Zhou, Lin Hero, Alfred |
author_facet | Zhou, Lin Hero, Alfred |
author_sort | Zhou, Lin |
collection | PubMed |
description | We consider the k-user successive refinement problem with causal decoder side information and derive an exponential strong converse theorem. The rate-distortion region for the problem can be derived as a straightforward extension of the two-user case by Maor and Merhav (2008). We show that for any rate-distortion tuple outside the rate-distortion region of the k-user successive refinement problem with causal decoder side information, the joint excess-distortion probability approaches one exponentially fast. Our proof follows by judiciously adapting the recently proposed strong converse technique by Oohama using the information spectrum method, the variational form of the rate-distortion region and Hölder’s inequality. The lossy source coding problem with causal decoder side information considered by El Gamal and Weissman is a special case ([Formula: see text]) of the current problem. Therefore, the exponential strong converse theorem for the El Gamal and Weissman problem follows as a corollary of our result. |
format | Online Article Text |
id | pubmed-7514900 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2019 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-75149002020-11-09 Exponential Strong Converse for Successive Refinement with Causal Decoder Side Information † Zhou, Lin Hero, Alfred Entropy (Basel) Article We consider the k-user successive refinement problem with causal decoder side information and derive an exponential strong converse theorem. The rate-distortion region for the problem can be derived as a straightforward extension of the two-user case by Maor and Merhav (2008). We show that for any rate-distortion tuple outside the rate-distortion region of the k-user successive refinement problem with causal decoder side information, the joint excess-distortion probability approaches one exponentially fast. Our proof follows by judiciously adapting the recently proposed strong converse technique by Oohama using the information spectrum method, the variational form of the rate-distortion region and Hölder’s inequality. The lossy source coding problem with causal decoder side information considered by El Gamal and Weissman is a special case ([Formula: see text]) of the current problem. Therefore, the exponential strong converse theorem for the El Gamal and Weissman problem follows as a corollary of our result. MDPI 2019-04-17 /pmc/articles/PMC7514900/ /pubmed/33267124 http://dx.doi.org/10.3390/e21040410 Text en © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Zhou, Lin Hero, Alfred Exponential Strong Converse for Successive Refinement with Causal Decoder Side Information † |
title | Exponential Strong Converse for Successive Refinement with Causal Decoder Side Information † |
title_full | Exponential Strong Converse for Successive Refinement with Causal Decoder Side Information † |
title_fullStr | Exponential Strong Converse for Successive Refinement with Causal Decoder Side Information † |
title_full_unstemmed | Exponential Strong Converse for Successive Refinement with Causal Decoder Side Information † |
title_short | Exponential Strong Converse for Successive Refinement with Causal Decoder Side Information † |
title_sort | exponential strong converse for successive refinement with causal decoder side information † |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514900/ https://www.ncbi.nlm.nih.gov/pubmed/33267124 http://dx.doi.org/10.3390/e21040410 |
work_keys_str_mv | AT zhoulin exponentialstrongconverseforsuccessiverefinementwithcausaldecodersideinformation AT heroalfred exponentialstrongconverseforsuccessiverefinementwithcausaldecodersideinformation |