  In this paper, we propose an approach to numerically compute the feedback
capacity of stationary finite dimensional Gaussian channels and construct
(arbitrarily close to) capacity-achieving feedback codes. In particular, we
first extend the interpretation of feedback communication over stationary
finite dimensional Gaussian channels as feedback control systems by showing
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 derived in [2].
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 finite dimensional 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 the sequence of lower bounds is
asymptotically capacity-achieving.
