Upper bounds on the capacity of discrete-time blockwise white Gaussian channels with feedback

Although it is well known that feedback does not increase the capacity of a n additive white Gaussian channel, Yanagi gave the necessary and sufficient condition under which thf capacity C-n,C- (FB)(P) Of a discrete time nonwh ite Gaussian channel is increased by feedback. In this correspondence we sh ow that the capacity C-n,C- FB(P) Of the Gaussian channel with feedback is a concave function of P, and give two types of inequalities: both 1/alpha C -n,C- FB(aP) and C-n,C- FB(alpha P) and C-n,C- FB(alpha P) + 1/2 ln 1/alpha are decreasing functions of alpha > 0. As their application we can obtain two upper bounds on the capacity of the discrete-time blockwise white Gauss ian channel with feedback. The results are quite useful when power constrai nt P is relatively not large.