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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
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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Conference Information
Committee IT  
Conference Date 2010-07-22 - 2010-07-23 
Place (in Japanese) (See Japanese page) 
Place (in English) Kogakuin University 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
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)  
Keyword(1) Minimal Forbidden Word  
Keyword(2) Antidictionary  
Keyword(3) Antidictionary Code  
Keyword(4) Data Compression  
Keyword(5) Almost Sure Convergence  
1st Author's Name Takahiro Ota  
1st Author's Affiliation Nagano Prefectural Institute of Technology (NPIT)
2nd Author's Name Hiroyoshi Morita  
2nd Author's Affiliation University of Electro-Communications (Univ. of Electro-Comm.)
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Date Time 2010-07-22 15:35:00 
Presentation Time 25 
Registration for IT 
Paper # IEICE-IT2010-20 
Volume (vol) IEICE-110 
Number (no) no.137 
Page pp.51-56 
#Pages IEICE-6 
Date of Issue IEICE-IT-2010-07-15 

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