On Renyi Entropy Power Inequalities

This paper gives improved Renyi entropy power inequalities (R-EPIs). Consider a sum S-n = Sigma(n)(k=1) x(k)of n independent continuous random vectors taking values on R-d, and let alpha epsilon [1, infinity]. An R-EPI provides a lower bound on the order-a Renyi entropy power of S-n, that, up to a multiplicative constant (which may depend in general on n, alpha, d), is equal to the sum of the order-alpha Renyi entropy powers of the n random vectors {X-k}(k=1)(n). For alpha = 1, the R-EPI coincides with the wellknown entropy power inequality by Shannon. The first improved R-EPI is obtained by tightening the recent R-EPI by Bobkov and Chistyakov, which relies on the sharpened Young's inequality. A further improvement of the R-EPI also relies on convex optimization and results on rank-one modification of a real valued diagonal matrix.