Prefixes and the entropy rate for long-range sources

Ioannis Kontoyiannis, Yurii M. Suhov

Research output: Contribution to conferencePaperpeer-review

1 Scopus citations

Abstract

The asymptotic a.s.-relation H = limn→∞ n log n ÷ Σi=1n Lin (X) is derived for any finite-valued stationary ergodic process X = (Xn, n ∈ Z) that satisfies a Doeblin-type condition: there exists r ≥ 1 such that essxinf P(Xn+r | x-∞,n) ≥ α > 0. Here, H is the entropy rate of the process X, and Lin(X) is the length of a shortest prefix in X which is initiated at time i and is not repeated among the prefixes initiated at times j, 1 ≤ i ≠ j ≤ n. The validity of this limiting result was established by Shields in 1989 for i.i.d. processes and also for irreducible aperiodic Markov chains. Under our new condition, we prove that this holds for a wider class of processes, that may have infinite memory.

Original languageEnglish (US)
StatePublished - 1994
EventProceedings of the 1994 IEEE International Symposium on Information Theory - Trodheim, Norw
Duration: Jun 27 1994Jul 1 1994

Other

OtherProceedings of the 1994 IEEE International Symposium on Information Theory
CityTrodheim, Norw
Period6/27/947/1/94

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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