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The entropies of the sum and the difference of two IID random variables are not too different

Madiman, M and Kontoyiannis, I (2010) The entropies of the sum and the difference of two IID random variables are not too different. In: UNSPECIFIED pp. 1369-1372..

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Abstract

Consider the entropy increase h(Y + Y′) - h(Y) of the sum of two continuous i.i.d. random variables Y,Y′, and the corresponding entropy increase h(Y - Y′) - h(Y) of their difference. We show that the ratio between these two quantities always lies between 1/2 and 2. This complements a recent result of Lapidoth and Pete, showing that the difference h(Y + Y′) -h(Y - Y′) may be arbitrarily large. Corresponding results are discussed for the discrete entropy, and connections are drawn with exciting recent mathematical work in the area of additive combinatorics. © 2010 IEEE.

Item Type: Conference or Workshop Item (UNSPECIFIED)
Subjects: UNSPECIFIED
Divisions: Div F > Signal Processing and Communications
Depositing User: Cron Job
Date Deposited: 08 Jan 2018 20:12
Last Modified: 27 Oct 2020 07:12
DOI: 10.1109/ISIT.2010.5513562