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Exponential Strong Converse for Successive Refinement with Causal Decoder Side Information

Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109, USA
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Part of this paper has been accepted to ISIT 2019, Paris, France.
Entropy 2019, 21(4), 410; https://doi.org/10.3390/e21040410
Received: 27 February 2019 / Revised: 9 April 2019 / Accepted: 13 April 2019 / Published: 17 April 2019
(This article belongs to the Special Issue Multiuser Information Theory II)
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Abstract

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 ( k = 1 ) of the current problem. Therefore, the exponential strong converse theorem for the El Gamal and Weissman problem follows as a corollary of our result. View Full-Text
Keywords: exponential strong converse; information spectrum method; successive refinement; causal side information exponential strong converse; information spectrum method; successive refinement; causal side information
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Zhou, L.; Hero, A. Exponential Strong Converse for Successive Refinement with Causal Decoder Side Information. Entropy 2019, 21, 410.

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