### Abstract

Original language | English |
---|---|

Title of host publication | Advances in electronics and electron physics |

Editors | Peter W. Hawkes |

Publisher | Elsevier |

Pages | 231-353 |

Number of pages | 123 |

Volume | 125 |

ISBN (Electronic) | 978-0-12-804815-3 |

ISBN (Print) | 978-0-12014767-0, 012014767X |

DOIs | |

Publication status | Published - 2002 |

### Publication series

Name | Advances in Imaging and Electron Physics |
---|---|

Volume | 125 |

ISSN (Print) | 1076-5670 |

### Fingerprint

### Bibliographical note

Copyright of Academic Press part of Elsevier Science### Keywords

- error-corrective codes
- replica-symmetry-breaking
- random energy model
- finite-connectivity systems
- spin-glasses
- belief propagation
- sparse matrices
- solvable model
- turbo codes
- phase

### Cite this

*Advances in electronics and electron physics*(Vol. 125, pp. 231-353). (Advances in Imaging and Electron Physics; Vol. 125). Elsevier. https://doi.org/10.1016/S1076-5670(02)80018-0

}

*Advances in electronics and electron physics.*vol. 125, Advances in Imaging and Electron Physics, vol. 125, Elsevier, pp. 231-353. https://doi.org/10.1016/S1076-5670(02)80018-0

**Low density parity check codes: a statistical physics perspective.** / Vicente, Renato; Saad, David; Kabashima, Yoshiyuki.

Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed)

TY - CHAP

T1 - Low density parity check codes: a statistical physics perspective

AU - Vicente, Renato

AU - Saad, David

AU - Kabashima, Yoshiyuki

N1 - Copyright of Academic Press part of Elsevier Science

PY - 2002

Y1 - 2002

N2 - The modem digital communication systems are made transmission reliable by employing error correction technique for the redundancies. Codes in the low-density parity-check work along the principles of Hamming code, and the parity-check matrix is very sparse, and multiple errors can be corrected. The sparseness of the matrix allows for the decoding process to be carried out by probability propagation methods similar to those employed in Turbo codes. The relation between spin systems in statistical physics and digital error correcting codes is based on the existence of a simple isomorphism between the additive Boolean group and the multiplicative binary group. Shannon proved general results on the natural limits of compression and error-correction by setting up the framework known as information theory. Error-correction codes are based on mapping the original space of words onto a higher dimensional space in such a way that the typical distance between encoded words increases.

AB - The modem digital communication systems are made transmission reliable by employing error correction technique for the redundancies. Codes in the low-density parity-check work along the principles of Hamming code, and the parity-check matrix is very sparse, and multiple errors can be corrected. The sparseness of the matrix allows for the decoding process to be carried out by probability propagation methods similar to those employed in Turbo codes. The relation between spin systems in statistical physics and digital error correcting codes is based on the existence of a simple isomorphism between the additive Boolean group and the multiplicative binary group. Shannon proved general results on the natural limits of compression and error-correction by setting up the framework known as information theory. Error-correction codes are based on mapping the original space of words onto a higher dimensional space in such a way that the typical distance between encoded words increases.

KW - error-corrective codes

KW - replica-symmetry-breaking

KW - random energy model

KW - finite-connectivity systems

KW - spin-glasses

KW - belief propagation

KW - sparse matrices

KW - solvable model

KW - turbo codes

KW - phase

UR - http://www.scopus.com/inward/record.url?scp=34247505045&partnerID=8YFLogxK

UR - https://www.sciencedirect.com/science/article/pii/S1076567002800180?via%3Dihub

U2 - 10.1016/S1076-5670(02)80018-0

DO - 10.1016/S1076-5670(02)80018-0

M3 - Chapter (peer-reviewed)

SN - 978-0-12014767-0

SN - 012014767X

VL - 125

T3 - Advances in Imaging and Electron Physics

SP - 231

EP - 353

BT - Advances in electronics and electron physics

A2 - Hawkes, Peter W.

PB - Elsevier

ER -