R\'enyi Entropy Power Inequalities via Normal Transport and Rotation
Information Theory
2018-10-17 v2 math.IT
Abstract
Following a recent proof of Shannon's entropy power inequality (EPI), a comprehensive framework for deriving various EPIs for the R\'enyi entropy is presented that uses transport arguments from normal densities and a change of variable by rotation. Simple arguments are given to recover the previously known R\'enyi EPIs and derive new ones, by unifying a multiplicative form with constant c and a modification with exponent {\alpha} of previous works. In particular, for log-concave densities, we obtain a simple transportation proof of a sharp varentropy bound.
Keywords
Cite
@article{arxiv.1807.02622,
title = {R\'enyi Entropy Power Inequalities via Normal Transport and Rotation},
author = {Olivier Rioul},
journal= {arXiv preprint arXiv:1807.02622},
year = {2018}
}
Comments
17 page. Entropy Journal, to appear