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 m denotes the message, Y(t) denotes the channel output at time t , Y_o ^ {t} denotes the sample path Y(\theta), 0 \leq \theta \leq t. W(t) is the Brownian motion representing noise, and \phi(s, y_o ^ {s} ,m) is the channel input (modulator output). It is shown that, under some general assumptions, the amount of mutual information I(Y_o ^{T} ,m) between the message m and the output path Y_o ^ {T} is directly related to the mean-square causal filtering error of estimating \phi (t, Y_o ^{t} ,m) from the received data Y_o ^{T} , 0 \leq t \leq T . It follows, as a corollary to the result for I(Y_o ^ {T} ,m) , that feedback can not increase the capacity of the nonband-limited additive white Gaussian noise channel.
['T. T. Kadota', 'Moshe Zakai', 'Jacob Ziv']
Mutual information of the white Gaussian channel with and without feedback