A Source Model With Probability Distribution over Word Set and Recurrence Time Theorem

  • GOTO Masayuki
    Faculty of Environmental and Information Studies, Musashi Institute of Technology
  • MATSUSHIMA Toshiyasu
    Department of the Industrial and Management Systems Engineering, School of Science and Engineering, Waseda University
  • HIRASAWA Shigeichi
    Department of the Industrial and Management Systems Engineering, School of Science and Engineering, Waseda University

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抄録

Nishiara and Morita defined an i. i. d. word-valued source which is defined as a pair of an i. i. d. source with a countable alphabet and a function which transforms each symbol into a word over finite alphabet. They showed the asymptotic equipartition property (AEP) of the i. i. d. word-valued source and discussed the relation with source coding algorithm based on a string parsing approach. However, their model is restricted in the i. i. d. case and any universal code for a class of word-valued sources isn't discussed. In this paper, we generalize the i. i. d. word-valued source to the ergodic word-valued source which is defined by an ergodic source with a countable alphabet and a function from each symbol to a word. We show existence of entropy rate of the ergodic word-valued source and its formula. Moreover, we show the recurrence time theorem for the ergodic word-valued source with a finite alphabet. This result clarifies that Ziv-Lempel code (ZL77 code) is universal for the ergodic word-valued source.

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詳細情報

  • CRID
    1571135652465560704
  • NII論文ID
    110003212514
  • NII書誌ID
    AA10826239
  • ISSN
    09168508
  • 本文言語コード
    en
  • データソース種別
    • CiNii Articles

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