TY - GEN
T1 - A simple proof of the entropy-power inequality via properties of mutual information
AU - Rioul, Olivier
PY - 2007/12/1
Y1 - 2007/12/1
N2 - While most useful information theoretic inequalities can be deduced from the basic properties of entropy or mutual information, Shannon's entropy power inequality (EPI) seems to be an exception: available information theoretic proofs of the EPI hinge on integral representations of differential entropy using either Fisher's information (FI) or minimum mean-square error (MMSE). In this paper, we first present a unified view of proofs via FI and MMSE, showing that they are essentially dual versions of the same proof, and then fill the gap by providing a new, simple proof of the EPI, which is solely based on the properties of mutual information and sidesteps both FI or MMSE representations.
AB - While most useful information theoretic inequalities can be deduced from the basic properties of entropy or mutual information, Shannon's entropy power inequality (EPI) seems to be an exception: available information theoretic proofs of the EPI hinge on integral representations of differential entropy using either Fisher's information (FI) or minimum mean-square error (MMSE). In this paper, we first present a unified view of proofs via FI and MMSE, showing that they are essentially dual versions of the same proof, and then fill the gap by providing a new, simple proof of the EPI, which is solely based on the properties of mutual information and sidesteps both FI or MMSE representations.
U2 - 10.1109/ISIT.2007.4557202
DO - 10.1109/ISIT.2007.4557202
M3 - Conference contribution
AN - SCOPUS:51649091459
SN - 1424414296
SN - 9781424414291
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 46
EP - 50
BT - Proceedings - 2007 IEEE International Symposium on Information Theory, ISIT 2007
T2 - 2007 IEEE International Symposium on Information Theory, ISIT 2007
Y2 - 24 June 2007 through 29 June 2007
ER -