Prefixes and the entropy rate for long-range sources

Ioannis Kontoyiannis, Iouri M. Soukhov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

The asymptotic a.s.-relation [eqution presented] 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 [eqution presented]. Here, H is the entropy rate of the process X, and Li n(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)
Title of host publicationProceedings - 1994 IEEE International Symposium on Information Theory, ISIT 1994
Number of pages1
DOIs
StatePublished - Dec 1 1994
Event1994 IEEE International Symposium on Information Theory, ISIT 1994 - Trondheim, Norway
Duration: Jun 27 1994Jul 1 1994

Other

Other1994 IEEE International Symposium on Information Theory, ISIT 1994
CountryNorway
CityTrondheim
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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    Kontoyiannis, I., & Soukhov, I. M. (1994). Prefixes and the entropy rate for long-range sources. In Proceedings - 1994 IEEE International Symposium on Information Theory, ISIT 1994 [394774] https://doi.org/10.1109/ISIT.1994.394774