On the capacity of the continuous time Gaussian channel with feedback

We discuss the capacity of the Gaussian channel with feedback. In general it is not easy to give an explicit formula for the capacity of a Gaussian channel, unless the channel is without feedback or a white Gaussian channel. We consider the case where a constraint, given in terms of the covariance functions of the input processes, is imposed on the input processes. It is shown that the capacity of the Gaussian channel can be achieved by transmitting a Gaussian message and using additive linear feedback.