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Entropy, Volume 20, Issue 9 (September 2018)
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Cover Story (view full-size image) Following a recent proof of Shannon’s entropy power inequality (EPI), a comprehensive framework for [...] Read more. 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 a of previous works. In particular, for log-concave densities, we obtain a simple transportation proof of a sharp varentropy bound. The figure shows a three dimensional plot of the quantity A(λ)/H(λ) to be minimized in order to derive some Rényi EPIs. View this paper.