Technical Program

Paper Detail

Paper Title An Elementary Proof of a Classical Information-Theoretic Formula
Paper IdentifierTU4.R9.4
Authors Xianming Liu, Huazhong University of Science and Technology, China; Ronit Bustin, Technion - Israel Institute of Technology, Israel; Guangyue Han, University of Hong Kong, Hong Kong SAR of China; Shlomo Shamai (Shitz), Technion - Israel Institute of Technology, Israel
Session Information Inequalities
Location Pontoise, Level 5
Session Time Tuesday, 09 July, 16:40 - 18:00
Presentation Time Tuesday, 09 July, 17:40 - 18:00
Manuscript  Click here to download the manuscript
Abstract A renowned information-theoretic formula by Shannon expresses the mutual information rate of a white Gaussian channel with a stationary Gaussian input as an integral of a simple function of the power spectral density of the channel input. We give in this paper a rigorous yet elementary proof of this classical formula. As opposed to all the conventional approaches, which either rely on heavy mathematical machineries or have to resort to some “external” results, our proof, which hinges on a recently proven sampling theorem, is elementary and self-contained, only using some well-known facts from basic calculus and matrix theory.