Paper Abstract and Keywords |
Presentation |
2010-07-22 15:35
An Almost Sure Convergence Proof of the Average Length of Minimal Forbidden Words on a Stationary Ergodic Source Takahiro Ota (NPIT), Hiroyoshi Morita (Univ. of Electro-Comm.) IT2010-20 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
An antidictionary is in particular useful for data compression, and it consists of minimal forbidden words for a given string. For a string $\mb{x}$ of length $n$ under a stationary ergodic source $\mathbf{X}$ with entropy rate $H(\mathbf{X}) < \infty$, it has been proved that $\log_{2} n / M(n, \mathbf{X}) = H(\mathbf{X})$ in probability, as $n \rightarrow \infty$, where $M(n, \mathbf{X})$ is the average length of minimal forbidden words for $\mathbf{X}$.
In this paper, we prove that the almost sure convergence instead of the convergence in probability. In other words, it is proved that $\Pr\{\lim_{n \rightarrow \infty} \log_{2} n / M(n, \mb{x}) = H(\mathbf{X})\} = 1$. Moreover, we propose that an algorithm to reconstruct a string $\mb{x}$ from its antidictionary $\mathcal{A}(\mb{x})$. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
Minimal Forbidden Word / Antidictionary / Antidictionary Code / Data Compression / Almost Sure Convergence / / / |
Reference Info. |
IEICE Tech. Rep., vol. 110, no. 137, IT2010-20, pp. 51-56, July 2010. |
Paper # |
IT2010-20 |
Date of Issue |
2010-07-15 (IT) |
ISSN |
Print edition: ISSN 0913-5685 Online edition: ISSN 2432-6380 |
Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) |
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IT2010-20 |
Conference Information |
Committee |
IT |
Conference Date |
2010-07-22 - 2010-07-23 |
Place (in Japanese) |
(See Japanese page) |
Place (in English) |
Kogakuin University |
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(See Japanese page) |
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Paper Information |
Registration To |
IT |
Conference Code |
2010-07-IT |
Language |
Japanese |
Title (in Japanese) |
(See Japanese page) |
Sub Title (in Japanese) |
(See Japanese page) |
Title (in English) |
An Almost Sure Convergence Proof of the Average Length of Minimal Forbidden Words on a Stationary Ergodic Source |
Sub Title (in English) |
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Minimal Forbidden Word |
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Antidictionary |
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Antidictionary Code |
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Data Compression |
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Almost Sure Convergence |
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1st Author's Name |
Takahiro Ota |
1st Author's Affiliation |
Nagano Prefectural Institute of Technology (NPIT) |
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Hiroyoshi Morita |
2nd Author's Affiliation |
University of Electro-Communications (Univ. of Electro-Comm.) |
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Speaker |
Author-1 |
Date Time |
2010-07-22 15:35:00 |
Presentation Time |
25 minutes |
Registration for |
IT |
Paper # |
IT2010-20 |
Volume (vol) |
vol.110 |
Number (no) |
no.137 |
Page |
pp.51-56 |
#Pages |
6 |
Date of Issue |
2010-07-15 (IT) |
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