Infinity-Rényi entropy power inequalities

Peng Xu; James Melbourne; Mokshay Madiman

doi:10.1109/ISIT.2017.8007077

Infinity-Rényi entropy power inequalities

Peng Xu, James Melbourne, Mokshay Madiman

Electrical and Computer Engineering

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

11 Scopus citations

Abstract

An optimal ∞-Rényi entropy power inequality is derived for d-dimensional random vectors. In fact, the authors establish a matrix ∞-EPI analogous to the generalization of the classical EPI established by Zamir and Feder. The result is achieved by demonstrating uniform distributions as extremizers of a certain class of ∞-Rényi entropy inequalities, and then putting forth a new rearrangement inequality for the ∞-Rényi entropy. Quantitative results are then derived as consequences of a new geometric inequality for uniform distributions on Euclidean balls.

Original language	English (US)
Title of host publication	2017 IEEE International Symposium on Information Theory, ISIT 2017
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2985-2989
Number of pages	5
ISBN (Electronic)	9781509040964
DOIs	https://doi.org/10.1109/ISIT.2017.8007077
State	Published - Aug 9 2017
Event	2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany Duration: Jun 25 2017 → Jun 30 2017

Publication series

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

Other

Other	2017 IEEE International Symposium on Information Theory, ISIT 2017
Country/Territory	Germany
City	Aachen
Period	6/25/17 → 6/30/17

Keywords

Infinity entropy power inequality
Information measures
Max density
Renyi entropy

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10.1109/ISIT.2017.8007077

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Infinity-Rényi entropy power inequalities. / Xu, Peng; Melbourne, James; Madiman, Mokshay.
2017 IEEE International Symposium on Information Theory, ISIT 2017. Institute of Electrical and Electronics Engineers Inc., 2017. p. 2985-2989 8007077 (IEEE International Symposium on Information Theory - Proceedings).

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

Xu, P, Melbourne, J & Madiman, M 2017, Infinity-Rényi entropy power inequalities. in 2017 IEEE International Symposium on Information Theory, ISIT 2017., 8007077, IEEE International Symposium on Information Theory - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 2985-2989, 2017 IEEE International Symposium on Information Theory, ISIT 2017, Aachen, Germany, 6/25/17. https://doi.org/10.1109/ISIT.2017.8007077

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Infinity-Rényi entropy power inequalities

Abstract

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Keywords

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