On the entropy power inequality for the rényi entropy of order [0, 1]

Arnaud Marsiglietti; James Melbourne

doi:10.1109/TIT.2018.2877741

On the entropy power inequality for the rényi entropy of order [0, 1]

Arnaud Marsiglietti, James Melbourne

Electrical and Computer Engineering

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

15 Scopus citations

Abstract

Using a sharp version of the reverse Young inequality, and a Rényi entropy comparison result due to Fradelizi, Madiman, and Wang (2016), the authors derive Rényi entropy power inequalities for log-concave random vectors when Rényi parameters belong to [0, 1]. Furthermore, the estimates are shown to be sharp up to absolute constants.

Original language	English (US)
Article number	8502868
Pages (from-to)	1387-1396
Number of pages	10
Journal	IEEE Transactions on Information Theory
Volume	65
Issue number	3
DOIs	https://doi.org/10.1109/TIT.2018.2877741
State	Published - Mar 2019

Bibliographical note

Funding Information:
Manuscript received November 10, 2017; revised July 20, 2018; accepted October 7, 2018. Date of publication October 23, 2018; date of current version February 14, 2019. A. Marsiglietti was supported by the Walter S. Baer and Jeri Weiss CMI Postdoctoral Fellowship. J. Melbourne was supported by NSF under Grant CNS 1544721 and Grant ECCS 1809194. This paper was presented at the 2018 IEEE International Symposium on Information Theory.

Publisher Copyright:
© 1963-2012 IEEE.

Keywords

Entropy power inequality
Rényi entropy
log-concave

Publisher link

10.1109/TIT.2018.2877741

Find It

Find It at U of M Libraries

Cite this

@article{c3f2c087143f43a4b30b77c463f7512e,

title = "On the entropy power inequality for the r{\'e}nyi entropy of order [0, 1]",

abstract = "Using a sharp version of the reverse Young inequality, and a R{\'e}nyi entropy comparison result due to Fradelizi, Madiman, and Wang (2016), the authors derive R{\'e}nyi entropy power inequalities for log-concave random vectors when R{\'e}nyi parameters belong to [0, 1]. Furthermore, the estimates are shown to be sharp up to absolute constants.",

keywords = "Entropy power inequality, R{\'e}nyi entropy, log-concave",

author = "Arnaud Marsiglietti and James Melbourne",

note = "Funding Information: Manuscript received November 10, 2017; revised July 20, 2018; accepted October 7, 2018. Date of publication October 23, 2018; date of current version February 14, 2019. A. Marsiglietti was supported by the Walter S. Baer and Jeri Weiss CMI Postdoctoral Fellowship. J. Melbourne was supported by NSF under Grant CNS 1544721 and Grant ECCS 1809194. This paper was presented at the 2018 IEEE International Symposium on Information Theory. Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",

year = "2019",

month = mar,

doi = "10.1109/TIT.2018.2877741",

language = "English (US)",

volume = "65",

pages = "1387--1396",

journal = "IEEE Transactions on Information Theory",

issn = "0018-9448",

publisher = "IEEE",

number = "3",

}

TY - JOUR

T1 - On the entropy power inequality for the rényi entropy of order [0, 1]

AU - Marsiglietti, Arnaud

AU - Melbourne, James

N1 - Funding Information: Manuscript received November 10, 2017; revised July 20, 2018; accepted October 7, 2018. Date of publication October 23, 2018; date of current version February 14, 2019. A. Marsiglietti was supported by the Walter S. Baer and Jeri Weiss CMI Postdoctoral Fellowship. J. Melbourne was supported by NSF under Grant CNS 1544721 and Grant ECCS 1809194. This paper was presented at the 2018 IEEE International Symposium on Information Theory. Publisher Copyright: © 1963-2012 IEEE.

PY - 2019/3

Y1 - 2019/3

N2 - Using a sharp version of the reverse Young inequality, and a Rényi entropy comparison result due to Fradelizi, Madiman, and Wang (2016), the authors derive Rényi entropy power inequalities for log-concave random vectors when Rényi parameters belong to [0, 1]. Furthermore, the estimates are shown to be sharp up to absolute constants.

AB - Using a sharp version of the reverse Young inequality, and a Rényi entropy comparison result due to Fradelizi, Madiman, and Wang (2016), the authors derive Rényi entropy power inequalities for log-concave random vectors when Rényi parameters belong to [0, 1]. Furthermore, the estimates are shown to be sharp up to absolute constants.

KW - Entropy power inequality

KW - Rényi entropy

KW - log-concave

UR - http://www.scopus.com/inward/record.url?scp=85055710993&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85055710993&partnerID=8YFLogxK

U2 - 10.1109/TIT.2018.2877741

DO - 10.1109/TIT.2018.2877741

M3 - Article

AN - SCOPUS:85055710993

SN - 0018-9448

VL - 65

SP - 1387

EP - 1396

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 3

M1 - 8502868

ER -

On the entropy power inequality for the rényi entropy of order [0, 1]

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this