Properties of a Word-Valued Source with a Non-prefix-free Word Set

Takashi ISHIDA; Masayuki GOTO; Toshiyasu MATSUSHIMA; Shigeichi HIRASAWA

doi:10.1093/ietfec/e89-a.12.3710

Properties of a Word-Valued Source with a Non-prefix-free Word Set

Takashi ISHIDA, Masayuki GOTO, Toshiyasu MATSUSHIMA, Shigeichi HIRASAWA

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Recently, a word-valued source has been proposed as a new class of information source models. A word-valued source is regarded as a source with a probability distribution over a word set. Although a word-valued source is a nonstationary source in general, it has been proved that an entropy rate of the source exists and the Asymptotic Equipartition Property (AEP) holds when the word set of the source is prefix-free. However, when the word set is not prefix-free (non-prefix-free), only an upper bound on the entropy density rate for an i.i.d. word-valued source has been derived so far. In this paper, we newly derive a lower bound on the entropy density rate for an i.i.d. word-valued source with a finite non-prefix-free word set. Then some numerical examples are given in order to investigate the behavior of the bounds.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E89-A No.12 pp.3710-3723

Publication Date: 2006/12/01

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Online ISSN: 1745-1337

DOI: 10.1093/ietfec/e89-a.12.3710

Type of Manuscript: PAPER

Category: Information Theory

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Takashi ISHIDA, Masayuki GOTO, Toshiyasu MATSUSHIMA, Shigeichi HIRASAWA, "Properties of a Word-Valued Source with a Non-prefix-free Word Set" in IEICE TRANSACTIONS on Fundamentals, vol. E89-A, no. 12, pp. 3710-3723, December 2006, doi: 10.1093/ietfec/e89-a.12.3710.
Abstract: Recently, a word-valued source has been proposed as a new class of information source models. A word-valued source is regarded as a source with a probability distribution over a word set. Although a word-valued source is a nonstationary source in general, it has been proved that an entropy rate of the source exists and the Asymptotic Equipartition Property (AEP) holds when the word set of the source is prefix-free. However, when the word set is not prefix-free (non-prefix-free), only an upper bound on the entropy density rate for an i.i.d. word-valued source has been derived so far. In this paper, we newly derive a lower bound on the entropy density rate for an i.i.d. word-valued source with a finite non-prefix-free word set. Then some numerical examples are given in order to investigate the behavior of the bounds.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e89-a.12.3710/_p

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@ARTICLE{e89-a_12_3710,
author={Takashi ISHIDA, Masayuki GOTO, Toshiyasu MATSUSHIMA, Shigeichi HIRASAWA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Properties of a Word-Valued Source with a Non-prefix-free Word Set},
year={2006},
volume={E89-A},
number={12},
pages={3710-3723},
abstract={Recently, a word-valued source has been proposed as a new class of information source models. A word-valued source is regarded as a source with a probability distribution over a word set. Although a word-valued source is a nonstationary source in general, it has been proved that an entropy rate of the source exists and the Asymptotic Equipartition Property (AEP) holds when the word set of the source is prefix-free. However, when the word set is not prefix-free (non-prefix-free), only an upper bound on the entropy density rate for an i.i.d. word-valued source has been derived so far. In this paper, we newly derive a lower bound on the entropy density rate for an i.i.d. word-valued source with a finite non-prefix-free word set. Then some numerical examples are given in order to investigate the behavior of the bounds.},
keywords={},
doi={10.1093/ietfec/e89-a.12.3710},
ISSN={1745-1337},
month={December},}

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TY - JOUR
TI - Properties of a Word-Valued Source with a Non-prefix-free Word Set
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 3710
EP - 3723
AU - Takashi ISHIDA
AU - Masayuki GOTO
AU - Toshiyasu MATSUSHIMA
AU - Shigeichi HIRASAWA
PY - 2006
DO - 10.1093/ietfec/e89-a.12.3710
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E89-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2006
AB - Recently, a word-valued source has been proposed as a new class of information source models. A word-valued source is regarded as a source with a probability distribution over a word set. Although a word-valued source is a nonstationary source in general, it has been proved that an entropy rate of the source exists and the Asymptotic Equipartition Property (AEP) holds when the word set of the source is prefix-free. However, when the word set is not prefix-free (non-prefix-free), only an upper bound on the entropy density rate for an i.i.d. word-valued source has been derived so far. In this paper, we newly derive a lower bound on the entropy density rate for an i.i.d. word-valued source with a finite non-prefix-free word set. Then some numerical examples are given in order to investigate the behavior of the bounds.
ER -