Control approach to computing the feedback capacity for stationary finite dimensional Gaussian channels

TL;DR

This paper links feedback communication over stationary Gaussian channels to control systems, providing methods to compute feedback capacity and construct capacity-achieving coding schemes through optimization of stabilizing controllers.

Contribution

It introduces a control-theoretic framework for feedback capacity computation and constructs practical coding schemes based on stabilizing feedback controllers.

Findings

Derived asymptotic capacity upper bounds via dual optimization.

Constructed feasible filters achieving lower bounds close to capacity.

Validated the approach with extensive examples showing asymptotic optimality.

Abstract

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.