Sufficient conditions for the equality of exact and Wyner common information

Badri N. Vellambi, Jorg Kliewer

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

7 Scopus citations

Abstract

The minimum common randomness required for the approximate and separate generation of a pair of correlated discrete memoryless sources is quantified by Wyner's notion of common information. Recently, Kumar, Li, and El Gamal introduced the notion of exact common information as the minimum common randomness required for the exact and separate generation of a pair of correlated discrete memoryless sources. This new notion of common information, which does not have a general single-letter characterization, was shown to match Wyner's notion for the symmetric binary erasure source. In this work, we present two conditions on the joint statistics of the pair of sources under either of which the exact and Wyner's notions of common information coincide. Though the conditions are implicit, we prove the equality of Wyner and exact common information for the generalized binary Z-source, generalized erasure source and the noisy typewriter source by establishing that these sources meet either of these conditions.

Original languageEnglish (US)
Title of host publication54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages370-377
Number of pages8
ISBN (Electronic)9781509045495
DOIs
StatePublished - Feb 10 2017
Event54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016 - Monticello, United States
Duration: Sep 27 2016Sep 30 2016

Publication series

Name54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016

Other

Other54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016
CountryUnited States
CityMonticello
Period9/27/169/30/16

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Computational Theory and Mathematics
  • Computer Networks and Communications
  • Hardware and Architecture
  • Control and Optimization

Keywords

  • Distributed source generation
  • Wyner common information
  • channel resolvability
  • exact common information
  • letter typicality

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