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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 SourceTakahiro 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 Copyrightandreproduction 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) Download PDF 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 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 Keyword(6) Keyword(7) Keyword(8) 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.) 3rd Author's Name 3rd Author's Affiliation () 4th Author's Name 4th Author's Affiliation () 5th Author's Name 5th Author's Affiliation () 6th Author's Name 6th Author's Affiliation () 7th Author's Name 7th Author's Affiliation () 8th Author's Name 8th Author's Affiliation () 9th Author's Name 9th Author's Affiliation () 10th Author's Name 10th Author's Affiliation () 11th Author's Name 11th Author's Affiliation () 12th Author's Name 12th Author's Affiliation () 13th Author's Name 13th Author's Affiliation () 14th Author's Name 14th Author's Affiliation () 15th Author's Name 15th Author's Affiliation () 16th Author's Name 16th Author's Affiliation () 17th Author's Name 17th Author's Affiliation () 18th Author's Name 18th Author's Affiliation () Speaker 1 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