Wyners common information for continuous random variables - A lossy source coding interpretation

Ge Xu, Wei Liu, Biao Chen

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Scopus citations

Abstract

Wyners common information can be easily generalized for continuous random variables. We provide an operational meaning for such generalization using the Gray-Wyner network with lossy source coding. Specifically, a Gray-Wyner network consists of one encoder and two decoders. A sequence of independent copies of a pair of random variables (X, Y) ∼ p(x, y) is encoded into three messages, one of them is a common input to both decoders. The two decoders attempt to reconstruct the two sequences respectively subject to individual distortion constraints. We show that Wyners common information equals the smallest common message rate when the total rate is arbitrarily close to the rate-distortion function with joint decoding. A surprising observation is that such equality holds independent of the values of distortion constraints as long as the distortions are less than certain thresholds. An interpretation for such thresholds is given for the symmetric case.

Original languageEnglish (US)
Title of host publication2011 45th Annual Conference on Information Sciences and Systems, CISS 2011
DOIs
StatePublished - 2011
Event2011 45th Annual Conference on Information Sciences and Systems, CISS 2011 - Baltimore, MD, United States
Duration: Mar 23 2011Mar 25 2011

Publication series

Name2011 45th Annual Conference on Information Sciences and Systems, CISS 2011

Other

Other2011 45th Annual Conference on Information Sciences and Systems, CISS 2011
CountryUnited States
CityBaltimore, MD
Period3/23/113/25/11

ASJC Scopus subject areas

  • Information Systems

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