OPERATOR INEQUALITY AND ITS APPLICATION TO CAPACITY OF GAUSSIAN CHANNEL

Abstract

We give some inequalities of capacity in Gaussian channel with or without feedback. The nonfeedback capacity $C_{n,Z}(P)$ and the feedback capacity $C_{n,FB,Z}(P)$ are both concave functions of $P$. Though it is shown that $C_{n,Z}(P)$ is a convex function of $Z$ in some sense, $C_{n,FB,Z}(P)$ is a convex-like function of $Z$.