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

Wasim Huleihel; Or Ordentlich

doi:10.1109/ISIT.2017.8006496

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 proceeding › Conference contribution › peer-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,...,x_n-1).

Original language	American English
Title of host publication	2017 IEEE International Symposium on Information Theory, ISIT 2017
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	91-95
Number of pages	5
ISBN (Electronic)	9781509040964
DOIs	https://doi.org/10.1109/ISIT.2017.8006496
State	Published - 9 Aug 2017
Externally published	Yes
Event	2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany Duration: 25 Jun 2017 → 30 Jun 2017

Publication series

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

Conference

Conference	2017 IEEE International Symposium on Information Theory, ISIT 2017
Country/Territory	Germany
City	Aachen
Period	25/06/17 → 30/06/17

Bibliographical note

Funding Information:
The work of WH and OO was supported by the MIT - Technion Postdoctoral Fellowship.

Publisher Copyright:
© 2017 IEEE.

Access to Document

10.1109/ISIT.2017.8006496

Cite this

Huleihel, W., & Ordentlich, O. (2017). How to quantize n outputs of a binary symmetric channel to n - 1 bits? In 2017 IEEE International Symposium on Information Theory, ISIT 2017 (pp. 91-95). Article 8006496 (IEEE International Symposium on Information Theory - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2017.8006496

@inproceedings{7da058404d2746feb5f1ab97f2b6d3fc,

title = "How to quantize n outputs of a binary symmetric channel to n - 1 bits?",

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).",

author = "Wasim Huleihel and Or Ordentlich",

note = "Funding Information: The work of WH and OO was supported by the MIT - Technion Postdoctoral Fellowship. Publisher Copyright: {\textcopyright} 2017 IEEE.; 2017 IEEE International Symposium on Information Theory, ISIT 2017 ; Conference date: 25-06-2017 Through 30-06-2017",

year = "2017",

month = aug,

day = "9",

doi = "10.1109/ISIT.2017.8006496",

language = "American English",

series = "IEEE International Symposium on Information Theory - Proceedings",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "91--95",

booktitle = "2017 IEEE International Symposium on Information Theory, ISIT 2017",

address = "United States",

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Huleihel, W & Ordentlich, O 2017, How to quantize n outputs of a binary symmetric channel to n - 1 bits? in 2017 IEEE International Symposium on Information Theory, ISIT 2017., 8006496, IEEE International Symposium on Information Theory - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 91-95, 2017 IEEE International Symposium on Information Theory, ISIT 2017, Aachen, Germany, 25/06/17. https://doi.org/10.1109/ISIT.2017.8006496

How to quantize n outputs of a binary symmetric channel to n - 1 bits? / Huleihel, Wasim; Ordentlich, Or.
2017 IEEE International Symposium on Information Theory, ISIT 2017. Institute of Electrical and Electronics Engineers Inc., 2017. p. 91-95 8006496 (IEEE International Symposium on Information Theory - Proceedings).

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