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• W2952065239 abstract "The entropy power inequality (EPI) provides lower bounds on the differential entropy of the sum of two independent real-valued random variables in terms of the individual entropies. Versions of the EPI for discrete random variables have been obtained for special families of distributions with the differential entropy replaced by the discrete entropy, but no universal inequality is known (beyond trivial ones). More recently, the sumset theory for the entropy function provides a sharp inequality $H(X+X')-H(X)geq 1/2 -o(1)$ when $X,X'$ are i.i.d. with high entropy. This paper provides the inequality $H(X+X')-H(X) geq g(H(X))$, where $X,X'$ are arbitrary i.i.d. integer-valued random variables and where $g$ is a universal strictly positive function on $mR_+$ satisfying $g(0)=0$. Extensions to non identically distributed random variables and to conditional entropies are also obtained." @default.
• W2952065239 created "2019-06-27" @default.
• W2952065239 creator A5025506109 @default.
• W2952065239 creator A5034537543 @default.
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• W2952065239 date "2013-01-17" @default.
• W2952065239 modified "2023-10-01" @default.
• W2952065239 title "A new entropy power inequality for integer-valued random variables" @default.
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• W2952065239 hasPublicationYear "2013" @default.
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