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Published December 2017 | Accepted Version
Journal Article Open

Variants of the Entropy Power Inequality

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.

Additional Information

© 2017 IEEE. 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. Communicated by P. Harremoës, Associate Editor for Probability and Statistics. The authors would like to thank Eric Carlen, Eshed Ram and Igal Sason for reading the manuscript and for their valuable comments. They are also grateful to both referees. In particular, one of them emphasized a dimension-free character of the optimal value of α , and the other one raised the problem of the monotonicity of the Rényi entropy in the central limit theorem.

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Additional details

Created:
August 19, 2023
Modified:
October 18, 2023