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Statistical Physics of Spin Glasses and Information ProcessingAn Introduction$
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Hidetoshi Nishimori

Print publication date: 2001

Print ISBN-13: 9780198509417

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198509417.001.0001

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Error-Correcting Codes

Error-Correcting Codes

Chapter:
(p.74) 5 Error-Correcting Codes
Source:
Statistical Physics of Spin Glasses and Information Processing
Author(s):

Hidetoshi Nishimori

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198509417.003.0005

Reliable transmission of information through noisy channels plays a vital role in modern society. Some aspects of this problem have close formal similarities to the theory of spin glasses. Noise in the transmission channel can be related to random interactions in spin glasses and the bit sequence representing information corresponds to the Ising spin configuration. The replica method serves as a powerful tool of analysis, and TAP-like equations can be used as a practical implementation of the algorithm to infer the original message. The gauge theory also provides an interesting point of view. This chapter introduces these problems.

Keywords:   error-correcting codes, signal transmission, noise, transmission channel, replica method

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