Second-order coding region for the discrete successive refinement source coding problem

2016 ◽  
Author(s):  
Lin Zhou ◽  
Vincent Y. F. Tan ◽  
Mehul Motani
Keyword(s):  
Source Coding ◽  
Second Order ◽  
Coding Region ◽  
Successive Refinement

scholarly journals Exponential Strong Converse for Successive Refinement with Causal Decoder Side Information

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 410
Author(s):  
Lin Zhou ◽  
Alfred Hero
Keyword(s):  
Current Problem ◽  
Source Coding ◽  
Side Information ◽  
Rate Distortion ◽  
Converse Theorem ◽  
Successive Refinement ◽  
Strong Converse Theorem ◽  
Variational Form ◽  
Strong Converse ◽  
Special Case

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.

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