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| Presentation | 2008-10-07 16:45 [Invited Talk] Gallager bound of channel coding and the replica method Yoshiyuki Kabashima (Tokyo Inst. Tech.)  IT2008-42 |
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| 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. |
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| 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 |
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| 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 |
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| Keyword(8) | |
| 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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