Optimal Transportation to the Entropy-Power Inequality

Abstract

We present a simple proof of the entropy-power inequality using an optimal transportation argument which takes the form of a simple change of variables. The same argument yields a reverse inequality involving a conditional differential entropy which has its own interest. It can also be generalized in various ways. The equality case is easily captured by this method and the proof is formally identical in one and several dimensions.

arXiv commentIEEE Information Theory and Applications Workshop (ITA 2017), San Diego, USA, Feb. 12-17, 2017