C. Mecklenbräuker:

"Proofs for the Maximum Entropy Property of the Normal Distribution";

Talk: Joint Workshop on Coding and Communications (JWCC), Santo Stefano Belbo, Piemonte, Italia (invited); 10-17-2010 - 10-19-2010; in: "Joint Workshop on Coding and Communications (JWCC 2010)", H. Bölcskei, E. Biglieri (ed.); (2010), 1 pages.

It is well known that for any absolutely continuous random variable, the distribution that maximizes the differential entropy subject to an upper bound sigma^2 on its second moment is the zero-mean normal distribution with variance sigma^2. In this contribution, several proofs for the maximum entropy property of the normal distribution are reviewed: Calculus of variations [Shannon,Kapur], use of Jensen's inequality [McEliece], and exploitation of the information inequality [Cover and Thomas], as well as Gallager's proof [Gallager]. The discussion emphasizes the corresponding concepts and pedagogical aspects.

Gaussian, Entropy, Calculus of Variations, Jensen's Inequality, Information Inequality

http://publik.tuwien.ac.at/files/PubDat_188432.pdf

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