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Paper Abstract and Keywords
Presentation 2008-10-07 16:45
[Invited Talk] Gallager bound of channel coding and the replica method
Yoshiyuki Kabashima (Tokyo Inst. Tech.) IT2008-42
Abstract (in Japanese) (See Japanese page) 
(in English) We explore the relationship between techniques of information theory and
statistical mechanics for assessing the performance of channel coding.
Our exploration is based on the framework developed by
Gallager in IEEE Trans. Inf. Theory 11, 3 (1965),
in which the minimum decoding error probability is upper-bounded by
an average of a generalized Chernoff's bound over a code ensemble.
We show that the resulting bound can be directly assessed by
the replica method of statistical mechanics, whereas further replacement
by another bound utilizing Jensen's inequality is necessary
in Gallager's original methodology. This associates a seemingly
ad hoc restriction on an adjustable parameter for optimizing the bound
with a phase transition between two analytic solutions
possibly dominating the bound.
The same approach improves the accuracy of performance assessment of
general code ensembles including the low density parity check codes,
although its mathematical justification is still open.
Keyword (in Japanese) (See Japanese page) 
(in English) channel coding / Gallager bound / error exponent / replica method / replica symmetry / / /  
Reference Info. IEICE Tech. Rep., vol. 108, no. 230, IT2008-42, pp. 23-28, Oct. 2008.
Paper # IT2008-42 
Date of Issue 2008-09-30 (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)
Download PDF IT2008-42

Conference Information
Committee IT  
Conference Date 2008-10-07 - 2008-10-07 
Place (in Japanese) (See Japanese page) 
Place (in English) Asaya Hotel(Kinugawa Onsen) 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To IT 
Conference Code 2008-10-IT 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Gallager bound of channel coding and the replica method 
Sub Title (in English)  
Keyword(1) channel coding  
Keyword(2) Gallager bound  
Keyword(3) error exponent  
Keyword(4) replica method  
Keyword(5) replica symmetry  
Keyword(6)  
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1st Author's Name Yoshiyuki Kabashima  
1st Author's Affiliation Tokyo Institute of Technology (Tokyo Inst. Tech.)
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Speaker Author-1 
Date Time 2008-10-07 16:45:00 
Presentation Time 55 minutes 
Registration for IT 
Paper # IT2008-42 
Volume (vol) vol.108 
Number (no) no.230 
Page pp.23-28 
#Pages 6 
Date of Issue 2008-09-30 (IT) 

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