A Source Model With Probability Distribution over Word Set and Recurrence Time Theorem
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- GOTO Masayuki
- Faculty of Environmental and Information Studies, Musashi Institute of Technology
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- MATSUSHIMA Toshiyasu
- Department of the Industrial and Management Systems Engineering, School of Science and Engineering, Waseda University
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- HIRASAWA Shigeichi
- Department of the Industrial and Management Systems Engineering, School of Science and Engineering, Waseda University
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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.
Journal
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- IEICE Trans. on Fundamentals, A
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IEICE Trans. on Fundamentals, A 86 (10), 2517-2525, 2003-10-01
The Institute of Electronics, Information and Communication Engineers
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Details 詳細情報について
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- CRID
- 1571135652465560704
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- NII Article ID
- 110003212514
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- NII Book ID
- AA10826239
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- ISSN
- 09168508
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- Text Lang
- en
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- Data Source
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- CiNii Articles