A binary analog to the entropy-power inequality

Let (X/sub n/), (Y/sub n/) be independent stationary binary random sequences with entropy H(X), H(Y), respectively. Let h( zeta )=- zeta log zeta -(1- zeta )log(1- zeta ), 0or= sigma (X)* sigma (Y), where sigma (Z)=h/sup -1/ (H(Z)), and alpha * beta = alpha (1- beta )+ beta (1- alpha ). When (Y/sub n/) are independent identically distributed, this reduces to Mrs. Gerber's Lemma from A.D. Wyner and J. Ziv (1973).<>