Asymptotic Synchronization for Finite-State Sources
Chaotic Dynamics
2015-05-20 v2 Information Theory
Dynamical Systems
math.IT
Machine Learning
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.
Keywords
Cite
@article{arxiv.1011.1581,
title = {Asymptotic Synchronization for Finite-State Sources},
author = {Nicholas F. Travers and James P. Crutchfield},
journal= {arXiv preprint arXiv:1011.1581},
year = {2015}
}
Comments
13 pages, 4 figures: http://cse.ucdavis.edu/~cmg/compmech/pubs/asfs.htm; updates and corrections added