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

Although it is well known that feedback does not increase capacity of an additive white Gaussian channel, Yanagi gave the necessary and sufficient condition under which the capacity Cn,FB(P ) of discrete time non-white Gaussian channel is increased by feedback. In this paper we show that the capacity Cn,FB(P ) of the Gaussian channel with feedback is a concave function of P , and give two type of inequalities: both 1 α Cn,FB(αP ) and Cn,FB(αP ) + 1 2 ln 1 α are decreasing functions of α > 0. As their application we can obtain two upper bounds on the capacity of discrete time blockwise white Gaussian channel with feedback. The results are quite useful when power constrant P is relatively not large. Running Head: Gaussian Channel Capacity with Feedback