Infinity-Rényi entropy power inequalities

Peng Xu, James Melbourne, Mokshay Madiman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 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 languageEnglish (US)
Title of host publication2017 IEEE International Symposium on Information Theory, ISIT 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2985-2989
Number of pages5
ISBN (Electronic)9781509040964
DOIs
StatePublished - Aug 9 2017
Event2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany
Duration: Jun 25 2017Jun 30 2017

Publication series

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

Other

Other2017 IEEE International Symposium on Information Theory, ISIT 2017
CountryGermany
CityAachen
Period6/25/176/30/17

Keywords

  • Infinity entropy power inequality
  • Information measures
  • Max density
  • Renyi entropy

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  • Cite this

    Xu, P., Melbourne, J., & Madiman, M. (2017). Infinity-Rényi entropy power inequalities. In 2017 IEEE International Symposium on Information Theory, ISIT 2017 (pp. 2985-2989). [8007077] (IEEE International Symposium on Information Theory - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2017.8007077