  We firstly 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
recently derived in [1]. The aforementioned interpretation provides an approach
to construct deterministic feedback coding schemes (with double exponential
decaying error probability). We next propose an asymptotic capacity-achieving
upper bounds, which can be numerically evaluated by solving finite dimensional
dual optimizations. From the filters that achieve upper bounds, we derive
feasible filters which lead to a sequence of lower bounds. Thus, from the lower
bound filters we obtain communication systems that achieve the lower bound
rate. Extensive examples show the sequence of lower bounds is asymptotic
capacity-achieving as well.
