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Mutual information of the white Gaussian channel with and without feedback

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3 Author(s)

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.

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Information Theory, IEEE Transactions on  (Volume:17 ,  Issue: 4 )