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 an additive white Gaussian channel, Yanagi (1992) gave the necessary and sufficient condition under which the capacity C_n,FB (P) of a discrete time nonwhite Gaussian channel is increased by feedback. In this correspondence we show that the capacity C_n,FB (P) of the Gaussian channel with feedback is a concave function of P, and give two types of inequalities: both 1/α C_n,FB(αP) and C_n,FB(αP)+½ln 1/α are decreasing functions of α>0. As their application we can obtain two upper bounds on the capacity of the discrete-time blockwise white Gaussian channel with feedback. The results are quite useful when power constraint P is relatively not large