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Code length between Markov processes

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Abstract

LetX 1 andX 2 be two mixing Markov shifts over finite alphabet. If the entropy ofX 1 is strictly larger than the entropy ofX 2, then there exists a finitary homomorphism ϕ:X 1→X 2 such that the code length is anL p random variable for allp<4/3. In particular, the expected length of the code ϕ is finite.

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References

  1. M. A. Akcoglu, A. del Junco and M. Rahe,Finitary codes between Markov processes, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete47 (1979), 305–314.

    Article  MATH  Google Scholar 

  2. S. N. Bernstein,Probability Theory (in Russian), Gosizdat, Moscow, 1927.

    Google Scholar 

  3. W. Feller,An Introduction to Probability Theory and Its Applications, Vol. 2, Wiley, New York, 1966.

    MATH  Google Scholar 

  4. T. Hamachi and M. S. Keane,Homomorphisms of noncommutative Bernoulli schemes, II. Finitary codes, preprint.

  5. M. Keane and M. Smorodinsky,A class of finitary codes, Israel Journal of Mathematics26 (1977), 352–371.

    Article  MATH  MathSciNet  Google Scholar 

  6. J. Serafin,The finitary coding of two Bernoulli schemes with unequal entropies has finite expectation, Indagationes Mathematicae. New Series7 (1996), 503–519.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland

    A. Iwanik & J. Serafin

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  1. A. Iwanik
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  2. J. Serafin
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Correspondence to A. Iwanik.

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Research supported by KBN grant 2 P03A 039 15 1998–2001.

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Iwanik, A., Serafin, J. Code length between Markov processes. Isr. J. Math. 111, 29–51 (1999). https://doi.org/10.1007/BF02810676

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  • DOI: https://doi.org/10.1007/BF02810676

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