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Rényi Entropy Power Inequalities via Normal Transport and Rotation (1807.02622v2)
Published 7 Jul 2018 in cs.IT and 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.