Asymptotic Synchronization for Finite-State Sources

TL;DR

This paper analyzes how observers synchronize with finite-state sources asymptotically, showing that uncertainty decreases exponentially, leading to accurate predictions of future outputs at the source entropy rate.

Contribution

It extends synchronization analysis from exact to nonexact finite-state sources, demonstrating exponential decay of uncertainty.

Findings

Observer's average uncertainty in source state vanishes exponentially

Uncertainty in predicting future output converges exponentially to source entropy rate

Synchronization occurs asymptotically for nonexact sources

Abstract

We extend a recent synchronization analysis of exact finite-state sources to nonexact sources for which synchronization occurs only asymptotically. Although the proof methods are quite different, the primary results remain the same. We find that an observer's average uncertainty in the source state vanishes exponentially fast and, as a consequence, an observer's average uncertainty in predicting future output converges exponentially fast to the source entropy rate.