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We consider the problem of optimal transmission of a set of correlated Gaussian signals through parallel channels with feedback. We send the signals by a linear encoding with output feedback. It is well-known that the optimal output feedback which minimizes the power of the encoded signal is given by the least-squares estimate of the linear term. Under a constraint on the total transmission power, we consider the problem of computing a set of gains for the channels which maximizes the mutual information between the output and the signal.

Optimal Transmission of a Set of Discrete-Time Gaussian Signals through Channels with Feedback