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Entropy 2015, 17(12), 8312-8324; doi:10.3390/e17127881

A New Tight Upper Bound on the Entropy of Sums

Department of Electrical and Computer Engineering, American University of Beirut, Beirut 1107 2020, Lebanon
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Academic Editor: Raúl Alcaraz Martínez
Received: 18 August 2015 / Revised: 8 December 2015 / Accepted: 14 December 2015 / Published: 19 December 2015
(This article belongs to the Section Information Theory)
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Abstract

We consider the independent sum of a given random variable with a Gaussian variable and an infinitely divisible one. We find a novel tight upper bound on the entropy of the sum which still holds when the variable possibly has an infinite second moment. The proven bound has several implications on both information theoretic problems and infinitely divisible noise channels’ transmission rates. View Full-Text
Keywords: entropy of sums; upper bound; infinite variance; infinitely divisible; differential entropy entropy of sums; upper bound; infinite variance; infinitely divisible; differential entropy
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Fahs, J.; Abou-Faycal, I. A New Tight Upper Bound on the Entropy of Sums. Entropy 2015, 17, 8312-8324.

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