Variants of the Entropy Power Inequality

An extension of the entropy power inequality to the form N
_r
^α
(X + Y) ≥ N
_r
^α
(X) + N
_r
^α
(Y) with arbitrary independent summands X and Y in R
ⁿ
is obtained for the Rényi entropy and powers α ≥ (r + 1)/2.