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Paper Abstract and Keywords
Presentation 2016-03-11 11:40
Asymptotics Zero Error Capacity on Nearest Neighbor Error Channels with Multilevel Alphabet
Takafumi Nakano, Tadashi Wadayama (NIT) IT2015-130 ISEC2015-89 WBS2015-113
Abstract (in Japanese) (See Japanese page) 
(in English) This paper evaluates the zero error capacity of Nearest Neighbor Error channels with multilevel alphabet (NNE channels). In the NNE channels, a transmitted sequence that is a $d$-tuple of a transmission alphabet. Only one error to a nearest neighbor symbol in a transmitted sequence can occur. The NNE channels can be considered as a limited magnitude error model, and closely relate to error models of flash memories. When $d=1$, the confusion graph of this channel is a perfect graph. Therefore the zero error capacity of this channel can be exactly evaluated. If $d ge 2$, the zero error capacity of these channels remains to be open. In this paper, we derive a lower bound of the zero error capacity of the NNE channels based on a result of the perfect Lee codes. The upper bound of the zero error capacity is derived from a feasible solution of a linear programming problem defined based on the confusion graph. As a result, a formula of the zero error capacity $Gamma(W) = d log_2 n + log_2 left(1/(2d+1) + mathcal{O}left(n^{-1}right)right)$ is obtained using the lower and upper bounds.
Keyword (in Japanese) (See Japanese page) 
(in English) Zero-error Capacity / Limited-Magnitude Error / Perfect Lee Code / / / / /  
Reference Info. IEICE Tech. Rep., vol. 115, no. 500, IT2015-130, pp. 175-180, March 2016.
Paper # IT2015-130 
Date of Issue 2016-03-03 (IT, ISEC, WBS) 
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)
Download PDF IT2015-130 ISEC2015-89 WBS2015-113

Conference Information
Committee IT ISEC WBS  
Conference Date 2016-03-10 - 2016-03-11 
Place (in Japanese) (See Japanese page) 
Place (in English) The University of Electro-Communications 
Topics (in Japanese) (See Japanese page) 
Topics (in English) joint meeting of IT, ISEC, and WBS 
Paper Information
Registration To IT 
Conference Code 2016-03-IT-ISEC-WBS 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Asymptotics Zero Error Capacity on Nearest Neighbor Error Channels with Multilevel Alphabet 
Sub Title (in English)  
Keyword(1) Zero-error Capacity  
Keyword(2) Limited-Magnitude Error  
Keyword(3) Perfect Lee Code  
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1st Author's Name Takafumi Nakano  
1st Author's Affiliation Nagoya Institute of technology (NIT)
2nd Author's Name Tadashi Wadayama  
2nd Author's Affiliation Nagoya Institute of technology (NIT)
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Speaker Author-1 
Date Time 2016-03-11 11:40:00 
Presentation Time 25 minutes 
Registration for IT 
Paper # IT2015-130, ISEC2015-89, WBS2015-113 
Volume (vol) vol.115 
Number (no) no.500(IT), no.501(ISEC), no.502(WBS) 
Page pp.175-180 
#Pages 6 
Date of Issue 2016-03-03 (IT, ISEC, WBS) 

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