Causal Posterior Matching and its Applications

TL;DR

This paper introduces a real-time causal posterior matching scheme for binary symmetric channels with feedback, providing analytical error guarantees and demonstrating its application in stabilizing control systems, outperforming some existing codes.

Contribution

It develops a real-time variant of Horstein's scheme with analytical error decay guarantees and applies it to control system stabilization over noisy channels.

Findings

Error probability decays exponentially with the scheme

The scheme effectively stabilizes unstable control plants

Empirical performance exceeds some existing reliable coding methods

Abstract

We consider the problem of communication over the binary symmetric channel with feedback, where the information sequence is made available in a causal, possibly random, fashion. We develop a real-time variant of the renowned Horstein scheme and provide analytical guarantees for its error-probability exponential decay rate. We further use the scheme to stabilize an unstable control plant over a binary symmetric channel and compare the analytical guarantees with its empirical performance as well as with those of anytime-reliable codes.