Feedback Capacity of Gaussian Channels Revisited

In this paper, we revisit the problem of finding the average capacity of the Gaussian feedback channel. First, we consider the problem of finding the average capacity of the analog colored Gaussian noise channel where the noise has an arbitrary spectral density. We introduce a new approach to the problem where we solve the problem over a finite number of transmissions and then consider the limit of the average capacity of the case of infinite number of transmissions. We then consider the important special case of stationary Gaussian noise with finite memory. We show that the channel capacity at stationarity can be found by solving a semi-definite program, and hence computationally tractable. We also give new proofs and structural results of the non stationary solution which bridges the gap between results in the literature for the stationary and non stationary feedback channel capacity.