Youla Coding and Computation of Gaussian Feedback Capacity

In this paper, we propose an approach to numerically compute the feedback capacity of stationary finite-dimensional (FD) Gaussian channels and construct (arbitrarily close to) capacity-achieving feedback codes. In particular, we first extend the interpretation of feedback communication over stationary FD Gaussian channels as feedback control systems. We show that the problem of finding stabilizing feedback controllers with maximal reliable transmission rate over Youla parameters coincides with the problem of finding strictly causal filters to achieve feedback capacity. This extended interpretation provides an approach to construct deterministic feedback coding schemes with double exponential decaying error probability. We next propose asymptotic capacity-achieving upper bounds, which can be numerically evaluated by solving FD convex optimizations. From the filters that achieve the upper bounds, we apply the Youla-based interpretation to construct feasible filters, i.e., feedback codes, leading to a sequence of lower bounds. We prove that the sequence of lower bounds is asymptotically capacity achieving.