### 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 |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Hardware and Architecture
- Information Systems

### Cite this

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

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

**A Source Model with Probability Distribution over Word Set and Recurrence Time Theorem.** / Goto, Masayuki; Matsushima, Toshiyasu; Hirasawa, Shigeichi.

Research output: Contribution to journal › Article

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*, vol. E86-A, no. 10, pp. 2517-2525.

}

TY - JOUR

T1 - A Source Model with Probability Distribution over Word Set and Recurrence Time Theorem

AU - Goto, Masayuki

AU - Matsushima, Toshiyasu

AU - Hirasawa, Shigeichi

PY - 2003/10

Y1 - 2003/10

N2 - 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.

AB - 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.

KW - Recurrence time

KW - Word sequences

KW - Word set

KW - Word-valued source

KW - Ziv-Lempel code

UR - http://www.scopus.com/inward/record.url?scp=0242496295&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0242496295&partnerID=8YFLogxK

M3 - Article

VL - E86-A

SP - 2517

EP - 2525

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

SN - 0916-8508

IS - 10

ER -