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

Masayuki Goto, Toshiyasu Matsushima, Shigeichi Hirasawa

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)2517-2525
Number of pages9
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE86-A
Issue number10
Publication statusPublished - 2003 Oct

Keywords

  • Recurrence time
  • Word sequences
  • Word set
  • Word-valued source
  • Ziv-Lempel code

ASJC Scopus subject areas

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics

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