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.
https://hal.telecom-paris.fr/hal-02287964 Contributor : TelecomParis HALConnect in order to contact the contributor Submitted on : Saturday, August 28, 2021 - 5:24:28 PM Last modification on : Wednesday, November 3, 2021 - 8:19:46 AM Long-term archiving on: : Monday, November 29, 2021 - 6:10:27 PM