Mutual information of the white Gaussian channel with and without feedback

The following model for the white Gaussian channel with or without feedback is considered: begin{equation} Y(t) = int_o ^{t} phi (s, Y_o ^{s} ,m) ds + W(t) end{equation} where denotes the message, denotes the channel output at time , denotes the sample path is the Brownian motion representing noise, and is the channel input (modulator output). It is shown that, under some general assumptions, the amount of mutual information between the message and the output path is directly related to the mean-square causal filtering error of estimating from the received data . It follows, as a corollary to the result for , that feedback can not increase the capacity of the nonband-limited additive white Gaussian noise channel.