Information Transmission over Continuous-Time Gaussian Channels with Feedback

We consider continuous-time Gaussian channels with feedback and investigate problems on the mutual information and the channel capacity. Whereas in most previous works some conditions are imposed on the Gaussian noise, in this paper we do not require any special conditions on the Gaussian noise. We derive a formula for the mutual information transmitted over the Gaussian channel with feedback. Then we show that the capacity of the channel is achieved in linear schemes, more precisely, achieved by sending a Gaussian message with the help of linear feedback. We also show some inequalities concerning the capacity of the channel.