Variants of the Entropy Power Inequality

Sergey G. Bobkov; Arnaud Marsiglietti

doi:10.1109/TIT.2017.2764487

Variants of the Entropy Power Inequality

Sergey G. Bobkov, Arnaud Marsiglietti

School of Mathematics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

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

Original language	English (US)
Article number	8076873
Pages (from-to)	7747-7752
Number of pages	6
Journal	IEEE Transactions on Information Theory
Volume	63
Issue number	12
DOIs	https://doi.org/10.1109/TIT.2017.2764487
State	Published - 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

Publisher Copyright:
© 1963-2012 IEEE.

Keywords

Entropy power inequality
Rényi entropy

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10.1109/TIT.2017.2764487

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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 R{\'e}nyi entropy and powers α ≥(r+1)/2.",

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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. Harremo{\"e}s, Associate Editor for Probability and Statistics. Digital Object Identifier 10.1109/TIT.2017.2764487 Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",

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Variants of the Entropy Power Inequality

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Bibliographical note

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