Variants of the Entropy Power Inequality

Sergey G. Bobkov, Arnaud Marsiglietti

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12 Scopus citations

Abstract

An extension of the entropy power inequality to the form Nrα (X+Y) ≥ Nrα (X) + Nrα (Y) with arbitrary independent summands X and Y in Rn is obtained for the Rényi entropy and powers α ≥(r+1)/2.

Original languageEnglish (US)
Article number8076873
Pages (from-to)7747-7752
Number of pages6
JournalIEEE Transactions on Information Theory
Volume63
Issue number12
DOIs
StatePublished - Dec 2017

Bibliographical note

Funding Information:
Manuscript received September 19, 2016; revised August 26, 2017; accepted October 11, 2017. Date of publication October 20, 2017; date of current version November 20, 2017. This work was supported in part by the Alexander von Humboldt Foundation, in part by NSF under Grant DMS-1612961, and in part by the Walter S. Baer and Jeri Weiss CMI Postdoctoral Fellowship. S. G. Bobkov is with the School of Mathematics, University of Minnesota, Minneapolis, MN 55455 USA (e-mail: bobkov@math.umn.edu). A. Marsiglietti is with the California Institute of Technology, Pasadena, CA 91125 USA. (e-mail: amarsigl@caltech.edu). Communicated by P. Harremoës, Associate Editor for Probability and Statistics. Digital Object Identifier 10.1109/TIT.2017.2764487

Keywords

  • Entropy power inequality
  • Rényi entropy

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