Journal of Statistical Physics

, Volume 145, Issue 5, pp 1202–1223 | Cite as

Asymptotic Synchronization for Finite-State Sources



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.


Entropy rate convergence Synchronization State estimation State uncertainty 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Nicholas F. Travers
    • 1
    • 2
  • James P. Crutchfield
    • 1
    • 2
    • 3
    • 4
  1. 1.Complexity Sciences CenterUniversity of California at DavisDavisUSA
  2. 2.Mathematics DepartmentUniversity of California at DavisDavisUSA
  3. 3.Physics DepartmentUniversity of California at DavisDavisUSA
  4. 4.Santa Fe InstituteSanta FeUSA

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