Youla Coding and Computation of Gaussian Feedback Capacity

TL;DR

This paper introduces a numerical method for computing the feedback capacity of Gaussian channels and constructing near-capacity feedback codes by extending control system interpretations and solving convex optimization problems.

Contribution

It extends the feedback communication interpretation as a control problem and provides a practical approach to design capacity-achieving feedback codes for Gaussian channels.

Findings

Numerical upper bounds for feedback capacity can be computed via convex optimization.

Constructed feedback codes approach the theoretical capacity asymptotically.

The method achieves double exponential decay in error probability.

Abstract

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.