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- W2071728535 abstract "Investigates the maximization of the differential entropy h(X+Y) of arbitrary dependent random variables X and Y under the constraints of fixed equal marginal densities for X and Y. We show that max[h(X+Y)]=h(2X), under the constraints that X and Y have the same fixed marginal density f, if and only if f is log-concave. The maximum is achieved when X=Y. If f is not log-concave, the maximum is strictly greater than h(2X). As an example, identically distributed Gaussian random variables have log-concave densities and satisfy max[h(X+Y)]=h(2X) with X=Y. More general inequalities in this direction should lead to capacity bounds for additive noise channels with feedback.< <ETX xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>></ETX>" @default.
- W2071728535 created "2016-06-24" @default.
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- W2071728535 date "1994-07-01" @default.
- W2071728535 modified "2023-09-26" @default.
- W2071728535 title "On the maximum entropy of the sum of two dependent random variables" @default.
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- W2071728535 doi "https://doi.org/10.1109/18.335945" @default.
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