Rényi Entropy Power Inequalities via Normal Transport and Rotation

Abstract

Following a recent proof of Shannon’s entropy power inequality (EPI), a comprehensive framework for deriving various EPIs for the Rényi 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 Rényi EPIs and derive new ones, by unifying a multiplicative form with constant c and a modification with exponent α of previous works. In particular, for log-concave densities, we obtain a simple transportation proof of a sharp varentropy bound.

Keywords

• Rényi entropy
• entropy power inequalities
• transportation arguments
• normal distributions
• escort distributions
• log-concave distributions