The optimal transmission of nonstationary Gaussian signals through parallel channels with feedback

We consider the problem of optimal transmission of correlated Gaussian signals through a set of parallel channels with feedback. The original signals are assumed to be given by a solution of a multi-dimensional linear stochastic differential equation and are sent by a linear encoding with output feedback. It is well known that the optimal output feedback, which maximizes the mutual information between the original signals, and the channel output is given by the least-squares estimate of the linear term. Under a constraint on the total power of the encoded signals, we compute a set of gains for the channels, which maximizes reduction of the estimation error.