Asymptotic Synchronization for Finite-State 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.

13 pages, 4 figures: http://cse.ucdavis.edu/~cmg/compmech/pubs/asfs.htm; updates and corrections added

References in corpus (2)

• Prediction, Retrodiction, and The Amount of Information Stored in the Present
• Exact Synchronization for Finite-State Sources

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• Thermodynamically-Efficient Local Computation and the Inefficiency of Quantum Memory Compression
• The fundamental thermodynamic bounds on finite models