Jump to ContentJump to Main Navigation
Information, Physics, and Computation$
Users without a subscription are not able to see the full content.

Marc Mézard and Andrea Montanari

Print publication date: 2009

Print ISBN-13: 9780198570837

Published to Oxford Scholarship Online: September 2009

DOI: 10.1093/acprof:oso/9780198570837.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2020. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 09 April 2020

Glassy states in coding theory

Glassy states in coding theory

(p.493) 21 Glassy states in coding theory
Information, Physics, and Computation

Marc Mézard

Andrea Montanari

Oxford University Press

In the limit of large block-length, iteratively decoded low density parity check (LDPC) codes exhibit two phase transitions. At low noise, the bit error rate under belief propagation decoding vanishes. In a second regime belief propagation decoding fails but maximum a posteriori probability (MAP) decoding succeeds. Finally above a second noise threshold decoding is impossible even with unbounded computational power. This chapter develops a common approach to these two transitions, through the study of ‘metastable’ configurations of the bits that are not codewords. It identifies the belief propagation phase transition with the onset of a dynamical glass phase, detected through the one step replica symmetry breaking approach. This is a structural phenomenon that spoils the performance of a large variety of decoders, from general iterative message passing schemes to simulated annealing.

Keywords:   decoding, low density parity check, code, LDPC, belief propagation, maximum a posteriori probability, MAP, glass, metastable

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .