Information-distilling quantizers

Bobak Nazer; Or Ordentlich; Yury Polyanskiy

doi:10.1109/ISIT.2017.8006497

Information-distilling quantizers

Bobak Nazer, Or Ordentlich, Yury Polyanskiy

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

18 Scopus citations

Abstract

Let X and Y be dependent random variables. We consider the problem of designing a scalar quantizer for Y to maximize the mutual information between its output and X, and study fundamental properties and bounds for this form of quantization. Our main focus is the regime of low I(X;Y), where we show that for a binary X, there always exists an M-level quantizer attaining mutual information of Ω(-M · I(X;Y)/log(I(X;Y)) and that there exist pairs of X, Y for which the mutual information attained by any M-level quantizer is O(-M · I(X; Y)/log(I(X; Y))).

Original language	English
Title of host publication	2017 IEEE International Symposium on Information Theory, ISIT 2017
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	96-100
Number of pages	5
ISBN (Electronic)	9781509040964
DOIs	https://doi.org/10.1109/ISIT.2017.8006497
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

Publisher Copyright:
© 2017 IEEE.

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10.1109/ISIT.2017.8006497

Cite this

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title = "Information-distilling quantizers",

abstract = "Let X and Y be dependent random variables. We consider the problem of designing a scalar quantizer for Y to maximize the mutual information between its output and X, and study fundamental properties and bounds for this form of quantization. Our main focus is the regime of low I(X;Y), where we show that for a binary X, there always exists an M-level quantizer attaining mutual information of Ω(-M · I(X;Y)/log(I(X;Y)) and that there exist pairs of X, Y for which the mutual information attained by any M-level quantizer is O(-M · I(X; Y)/log(I(X; Y))).",

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Nazer, B, Ordentlich, O & Polyanskiy, Y 2017, Information-distilling quantizers. in 2017 IEEE International Symposium on Information Theory, ISIT 2017., 8006497, IEEE International Symposium on Information Theory - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 96-100, 2017 IEEE International Symposium on Information Theory, ISIT 2017, Aachen, Germany, 25/06/17. https://doi.org/10.1109/ISIT.2017.8006497

Information-distilling quantizers. / Nazer, Bobak; Ordentlich, Or; Polyanskiy, Yury.
2017 IEEE International Symposium on Information Theory, ISIT 2017. Institute of Electrical and Electronics Engineers Inc., 2017. p. 96-100 8006497 (IEEE International Symposium on Information Theory - Proceedings).

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

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AB - Let X and Y be dependent random variables. We consider the problem of designing a scalar quantizer for Y to maximize the mutual information between its output and X, and study fundamental properties and bounds for this form of quantization. Our main focus is the regime of low I(X;Y), where we show that for a binary X, there always exists an M-level quantizer attaining mutual information of Ω(-M · I(X;Y)/log(I(X;Y)) and that there exist pairs of X, Y for which the mutual information attained by any M-level quantizer is O(-M · I(X; Y)/log(I(X; Y))).

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Information-distilling quantizers

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