2022
DOI: 10.1093/imaiai/iaab021
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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 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 commun… Show more

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Cited by 2 publications
(1 citation statement)
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“…Notice that if δ = 0, this quantity particularizes to the usual Wyner's common information as the constraint I(X; Y |W ) ≤ δ reduces to the Markovity constraint X − W − Y . In another recent work, Graczyk, Lapidoth, and Wigger [67] defined a conditional version of Wyner's common information…”
Section: Generalizations and Applicationsmentioning
confidence: 99%
“…Notice that if δ = 0, this quantity particularizes to the usual Wyner's common information as the constraint I(X; Y |W ) ≤ δ reduces to the Markovity constraint X − W − Y . In another recent work, Graczyk, Lapidoth, and Wigger [67] defined a conditional version of Wyner's common information…”
Section: Generalizations and Applicationsmentioning
confidence: 99%