How to quantize n outputs of a binary symmetric channel to n - 1 bits?

Wasim Huleihel, Or Ordentlich

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

4 Scopus citations

Abstract

Suppose that Yn is obtained by observing a uniform Bernoulli random vector Xn through a binary symmetric channel with crossover probability α. The "most informative Boolean function" conjecture postulates that the maximal mutual information between Yn and any Boolean function b(Xn) is attained by a dictator function. In this paper, we consider the "complementary" case in which the Boolean function is replaced by f: {0, 1}n → {0,1}n, namely, an n - 1 bit quantizer, and show that I(f(Xn);Yn) < (n - 1) • (1 - h(α)) for any such f. Thus, in this case, the optimal function is of the form f(xn) = (x1,...,xn-1).

Original languageAmerican English
Title of host publication2017 IEEE International Symposium on Information Theory, ISIT 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages91-95
Number of pages5
ISBN (Electronic)9781509040964
DOIs
StatePublished - 9 Aug 2017
Externally publishedYes
Event2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany
Duration: 25 Jun 201730 Jun 2017

Publication series

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

Conference

Conference2017 IEEE International Symposium on Information Theory, ISIT 2017
Country/TerritoryGermany
CityAachen
Period25/06/1730/06/17

Bibliographical note

Publisher Copyright:
© 2017 IEEE.

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