Exponential Strong Converse for Successive Refinement with Causal Decoder Side Information
Abstract
We consider the kuser successive refinement problem with causal decoder side information and derive an exponential strong converse theorem. The ratedistortion region for the problem can be derived as a straightforward extension of the twouser case by Maor and Merhav (2008). We show that for any ratedistortion tuple outside the ratedistortion region of the kuser successive refinement problem with causal decoder side information, the joint excessdistortion 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 ratedistortion 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.
 Publication:

Entropy
 Pub Date:
 April 2019
 DOI:
 10.3390/e21040410
 arXiv:
 arXiv:1901.01356
 Bibcode:
 2019Entrp..21..410Z
 Keywords:

 exponential strong converse;
 information spectrum method;
 successive refinement;
 causal side information;
 Computer Science  Information Theory
 EPrint:
 doi:10.3390/e21040410