### 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 language | English |
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Pages (from-to) | 2517-2525 |

Number of pages | 9 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E86-A |

Issue number | 10 |

Publication status | Published - 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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## Cite this

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*,

*E86-A*(10), 2517-2525.