Conditional and Relevant Common Information

Abstract Two variations on Wyner’s common information are proposed: conditional common information and relevant common information. These are shown to have operational meanings analogous to those of Wyner’s common information in appropriately defined distributed problems of compression, simulation a...

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Bibliographic Details
Published inInformation and Inference: A Journal of the IMA Vol. 11; no. 2; pp. 679 - 737
Main Authors Graczyk, Robert, Lapidoth, Amos, Wigger, Michèle
Format Journal Article
LanguageEnglish
Published Oxford University Press 11.06.2022
Oxford University Press (OUP)
Subjects
Computer Science
Information Theory
Distributed Source Coding
Coordination
Simulation
Channel Synthesis
Common Information
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Summary:Abstract Two variations on Wyner’s common information are proposed: conditional common information and relevant common information. These are shown to have operational meanings analogous to those of Wyner’s common information in appropriately defined distributed problems of compression, simulation and channel synthesis. For relevant common information, an additional operational meaning is identified: on a multiple-access channel with private and common messages, it is the minimal common-message rate that enables communication at the maximum sum-rate under a weak coordination constraint on the inputs and output. En route, the weak-coordination problem over a Gray-Wyner network is solved under the no-excess-rate constraint.
ISSN:2049-8764
2049-8772
DOI:10.1093/imaiai/iaab021