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Paper Abstract and Keywords
Presentation 2025-05-30 10:00
Isomorphism of Shannon Covers of Periodic-Finite-Type Shifts Characterized by a Single Forbidden Word
Haruki Makuta, Akiko Manada (NUT) IT2025-11 EMM2025-11
Abstract (in Japanese) (See Japanese page) 
(in English) To improve the reliability of storage media, constraints, such as limiting runs of the same symbol, have been applied to sequences.As an extension of constraints, a Periodic-Finite-Type Shift defined by a finite set of periodically forbidden words has been introduced.When encoding any sequence into an allowed sequence that satisfies these constraints, the maximum coding rate is an important measure of efficiency. If a set of allowed sequences is represented by a labeled directed graph called a presentation, the maximum coding rate can be calculated from the largest eigenvalue of its adjacency matrix. Among such presentations, a presentation with the smallest number of vertices is called a Shannon cover. The Shannon cover is a canonical presentation, and is important from the perspective of the computational cost of the maximum coding rate. This paper investigates the case where a Periodic-Finite-Type shift is characterized by a single forbidden word.We present two results from the perspective of presentations. First, we show that the Shannon cover can be obtained using the algorithm proposed by Béal et al. Second, we clarify the graph isomorphism of presentations generated from De Bruijn graphs. Based on these results, we discusses the number of distinct maximum coding rates.
Keyword (in Japanese) (See Japanese page) 
(in English) Periodic-Finite-Type shift / Presentation / Shannon cover / Graph isomorphism / Maximum coding rate / / /  
Reference Info. IEICE Tech. Rep., vol. 125, no. 37, IT2025-11, pp. 56-61, May 2025.
Paper # IT2025-11 
Date of Issue 2025-05-22 (IT, EMM) 
ISSN 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)
Download PDF IT2025-11 EMM2025-11

Conference Information
Committee IT EMM  
Conference Date 2025-05-29 - 2025-05-30 
Place (in Japanese) (See Japanese page) 
Place (in English) Nagasaki University 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Information Security, Information Theory, Information Hiding, etc., Freshman session 
Paper Information
Registration To IT 
Conference Code 2025-05-IT-EMM 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Isomorphism of Shannon Covers of Periodic-Finite-Type Shifts Characterized by a Single Forbidden Word 
Sub Title (in English)  
Keyword(1) Periodic-Finite-Type shift  
Keyword(2) Presentation  
Keyword(3) Shannon cover  
Keyword(4) Graph isomorphism  
Keyword(5) Maximum coding rate  
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1st Author's Name Haruki Makuta  
1st Author's Affiliation Nagaoka University of Technology (NUT)
2nd Author's Name Akiko Manada  
2nd Author's Affiliation Nagaoka University of Technology (NUT)
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Speaker Author-1 
Date Time 2025-05-30 10:00:00 
Presentation Time 25 minutes 
Registration for IT 
Paper # IT2025-11, EMM2025-11 
Volume (vol) vol.125 
Number (no) no.37(IT), no.38(EMM) 
Page pp.56-61 
#Pages 6 
Date of Issue 2025-05-22 (IT, EMM) 

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