A strong converse for a collection of network source coding problems

Authors:
WeiHsin Gu;Michelle Effros
Affiliations:
Department of Electrical Engineering, California Institute of Technology, Pasadena, CA;Department of Electrical Engineering, California Institute of Technology, Pasadena, CA
Venue:
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Year:
2009

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Abstract

We prove a strong converse for particular source coding problems: the Ahlswede-Körner (coded side information) problem, lossless source coding for multicast networks with side-information at the end nodes, and the Gray-Wyner problem. Source and side-information sequences are drawn i.i.d. according to a given distribution on a finite alphabet. The strong converse discussed here states that when a given rate vector R is not D-achievable, the probability of observing distortion D for any sequence of block codes at rate R must decrease exponentially to 0 as the block length grows without bound. This strong converse implies the prior strong converses for the point-to-point network, Slepian-Wolf problem, and Ahlswede-Körner (coded side information) problem.