Optimal transport to the entropy power inequality – Olivier Rioul

Olivier Rioul
Télécom Paris, LTCI, Palaiseau
https://perso.telecom-paristech.fr/rioul/

Date(s) : 13/01/2017   iCal
11 h 00 min - 12 h 00 min

The Entropy Power Inequality (EPI) has a long history. It was first stated by Shannon in his famous 1948 seminal paper, the founding work of the field of information theory. It was much later proved by Stam using Fisher’s information and by Lieb using Young’s convolutional inequality with sharp constant. Today’ available proofs are variations of these two proofs. In this talk, we first motivate the use of the EPI for communication theory. After reviewing previous proofs, we introduce an optimal transport argument that recently proved useful in information theory. This takes the form of a simple change of variables from which we build an elementary proof of the EPI that opens new perspectives.

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