Talks and Poster Presentations (with Proceedings-Entry):
"Proofs for the Maximum Entropy Property of the Normal Distribution";
Talk: Joint Workshop on Coding and Communications (JWCC),
Santo Stefano Belbo, Piemonte, Italia (invited);
- 10-19-2010; in: "Joint Workshop on Coding and Communications (JWCC 2010)",
H. Bölcskei, E. Biglieri (ed.);
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
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.