TY - GEN
T1 - An Elementary Proof of a Classical Information-Theoretic Formula
AU - Liu, Xianming
AU - Busting, Ronit
AU - Han, Guangyue
AU - Shitz, Shlomo Shamai
N1 - Publisher Copyright: © 2019 IEEE.
PY - 2019/7
Y1 - 2019/7
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85073162011&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2019.8849415
DO - 10.1109/ISIT.2019.8849415
M3 - منشور من مؤتمر
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1392
EP - 1396
BT - 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
T2 - 2019 IEEE International Symposium on Information Theory, ISIT 2019
Y2 - 7 July 2019 through 12 July 2019
ER -