An improved upper bound for the most informative boolean function conjecture

Or Ordentlich, Ofer Shayevitz, Omri Weinstein

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

8 Scopus citations

Abstract

Suppose X is a uniformly distributed n-dimensional binary vector and Y is obtained by passing X through a binary symmetric channel with crossover probability α. A recent conjecture by Courtade and Kumar postulates that I(F(X); Y ) ≤ 1 - h(α) for any Boolean function F. So far, the best known upper bound was essentially I(F(X); Y ) ≤ (1 - 2α)2. In this paper, we derive a new upper bound that holds for all balanced functions, and improves upon the best known previous bound for α > 1 over 3.

Original languageAmerican English
Title of host publicationProceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages500-504
Number of pages5
ISBN (Electronic)9781509018062
DOIs
StatePublished - 10 Aug 2016
Externally publishedYes
Event2016 IEEE International Symposium on Information Theory, ISIT 2016 - Barcelona, Spain
Duration: 10 Jul 201615 Jul 2016

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2016-August
ISSN (Print)2157-8095

Conference

Conference2016 IEEE International Symposium on Information Theory, ISIT 2016
Country/TerritorySpain
CityBarcelona
Period10/07/1615/07/16

Bibliographical note

Publisher Copyright:
© 2016 IEEE.

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