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.
Bibliographical noteFunding 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: firstname.lastname@example.org). A. Marsiglietti is with the California Institute of Technology, Pasadena, CA 91125 USA. (e-mail: email@example.com). Communicated by P. Harremoës, Associate Editor for Probability and Statistics. Digital Object Identifier 10.1109/TIT.2017.2764487
- Entropy power inequality
- Rényi entropy