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It is well known that the problem of computing the feedback capacity of astationary Gaussian channel can be recast as an infinite-dimensionaloptimization problem; moreover, necessary and sufficient conditions for theoptimality of a solution to this optimization problem have been characterized,and based on this characterization, an explicit formula for the feedbackcapacity has been given for the case that the noise is a first-orderautoregressive moving-average Gaussian process. In this paper, we furtherexamine the above-mentioned infinite-dimensional optimization problem. We provethat unless the Gaussian noise is white, its optimal solution is unique, and wepropose an algorithm to recursively compute the unique optimal solution, whichis guaranteed to converge in theory and features an efficient implementationfor a suboptimal solution in practice. Furthermore, for the case that the noiseis a k-th order autoregressive moving-average Gaussian process, we give arelatively more explicit formula for the feedback capacity; more specifically,the feedback capacity is expressed as a simple function evaluated at a solutionto a system of polynomial equations, which is amenable to numerical computationfor the cases k=1, 2 and possibly beyond.

Feedback Capacity of Stationary Gaussian Channels Further Examined