An improved upper bound for the most informative boolean function conjecture

Or Ordentlich; Ofer Shayevitz; Omri Weinstein

doi:10.1109/ISIT.2016.7541349

An improved upper bound for the most informative boolean function conjecture

Or Ordentlich
, Ofer Shayevitz
, Omri Weinstein

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-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 language	English
Title of host publication	Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	500-504
Number of pages	5
ISBN (Electronic)	9781509018062
DOIs	https://doi.org/10.1109/ISIT.2016.7541349
State	Published - 10 Aug 2016
Externally published	Yes
Event	2016 IEEE International Symposium on Information Theory, ISIT 2016 - Barcelona, Spain Duration: 10 Jul 2016 → 15 Jul 2016

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2016-August
ISSN (Print)	2157-8095

Conference

Conference	2016 IEEE International Symposium on Information Theory, ISIT 2016
Country/Territory	Spain
City	Barcelona
Period	10/07/16 → 15/07/16

Bibliographical note

Publisher Copyright:
© 2016 IEEE.

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10.1109/ISIT.2016.7541349

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Ordentlich, O., Shayevitz, O., & Weinstein, O. (2016). An improved upper bound for the most informative boolean function conjecture. In Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory (pp. 500-504). Article 7541349 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2016-August). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2016.7541349

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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.",

author = "Or Ordentlich and Ofer Shayevitz and Omri Weinstein",

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doi = "10.1109/ISIT.2016.7541349",

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Ordentlich, O, Shayevitz, O & Weinstein, O 2016, An improved upper bound for the most informative boolean function conjecture. in Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory., 7541349, IEEE International Symposium on Information Theory - Proceedings, vol. 2016-August, Institute of Electrical and Electronics Engineers Inc., pp. 500-504, 2016 IEEE International Symposium on Information Theory, ISIT 2016, Barcelona, Spain, 10/07/16. https://doi.org/10.1109/ISIT.2016.7541349

An improved upper bound for the most informative boolean function conjecture. / Ordentlich, Or; Shayevitz, Ofer; Weinstein, Omri.
Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory. Institute of Electrical and Electronics Engineers Inc., 2016. p. 500-504 7541349 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2016-August).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Ordentlich O, Shayevitz O, Weinstein O. An improved upper bound for the most informative boolean function conjecture. In Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory. Institute of Electrical and Electronics Engineers Inc. 2016. p. 500-504. 7541349. (IEEE International Symposium on Information Theory - Proceedings). doi: 10.1109/ISIT.2016.7541349

An improved upper bound for the most informative boolean function conjecture

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