### Abstract

We present a method to construct low-density parity-check (LDPC) codes with low error floors on the binary symmetric channel. Codes are constructed so that their Tanner graphs are free of certain small trapping sets. These trapping sets are selected from the trapping set ontology for the Gallager A/B decoder. They are selected based on their relative harmfulness for a given decoding algorithm. We evaluate the relative harmfulness of different trapping sets for the sum-product algorithm by using the topological relations among them and by analyzing the decoding failures on one trapping set in the presence or absence of other trapping sets. We apply this method to construct structured LDPC codes. To facilitate the discussion, we give a new description of structured LDPC codes whose parity-check matrices are arrays of permutation matrices. This description uses Latin squares to define a set of permutation matrices that have disjoint support and to derive a simple necessary and sufficient condition for the Tanner graph of a code to be free of four cycles.

Original language | English (US) |
---|---|

Article number | 6169192 |

Pages (from-to) | 2280-2302 |

Number of pages | 23 |

Journal | IEEE Transactions on Information Theory |

Volume | 58 |

Issue number | 4 |

DOIs | |

State | Published - Apr 2012 |

### Fingerprint

### Keywords

- Error floor
- Latin squares
- structured low-density parity-check codes
- trapping sets

### ASJC Scopus subject areas

- Information Systems
- Computer Science Applications
- Library and Information Sciences

### Cite this

*IEEE Transactions on Information Theory*,

*58*(4), 2280-2302. [6169192]. https://doi.org/10.1109/TIT.2011.2173733

**On the construction of structured LDPC codes free of small trapping sets.** / Nguyen, Dung Viet; Chilappagari, Shashi Kiran; Marcellin, Michael W; Vasic, Bane V.

Research output: Contribution to journal › Article

*IEEE Transactions on Information Theory*, vol. 58, no. 4, 6169192, pp. 2280-2302. https://doi.org/10.1109/TIT.2011.2173733

}

TY - JOUR

T1 - On the construction of structured LDPC codes free of small trapping sets

AU - Nguyen, Dung Viet

AU - Chilappagari, Shashi Kiran

AU - Marcellin, Michael W

AU - Vasic, Bane V

PY - 2012/4

Y1 - 2012/4

N2 - We present a method to construct low-density parity-check (LDPC) codes with low error floors on the binary symmetric channel. Codes are constructed so that their Tanner graphs are free of certain small trapping sets. These trapping sets are selected from the trapping set ontology for the Gallager A/B decoder. They are selected based on their relative harmfulness for a given decoding algorithm. We evaluate the relative harmfulness of different trapping sets for the sum-product algorithm by using the topological relations among them and by analyzing the decoding failures on one trapping set in the presence or absence of other trapping sets. We apply this method to construct structured LDPC codes. To facilitate the discussion, we give a new description of structured LDPC codes whose parity-check matrices are arrays of permutation matrices. This description uses Latin squares to define a set of permutation matrices that have disjoint support and to derive a simple necessary and sufficient condition for the Tanner graph of a code to be free of four cycles.

AB - We present a method to construct low-density parity-check (LDPC) codes with low error floors on the binary symmetric channel. Codes are constructed so that their Tanner graphs are free of certain small trapping sets. These trapping sets are selected from the trapping set ontology for the Gallager A/B decoder. They are selected based on their relative harmfulness for a given decoding algorithm. We evaluate the relative harmfulness of different trapping sets for the sum-product algorithm by using the topological relations among them and by analyzing the decoding failures on one trapping set in the presence or absence of other trapping sets. We apply this method to construct structured LDPC codes. To facilitate the discussion, we give a new description of structured LDPC codes whose parity-check matrices are arrays of permutation matrices. This description uses Latin squares to define a set of permutation matrices that have disjoint support and to derive a simple necessary and sufficient condition for the Tanner graph of a code to be free of four cycles.

KW - Error floor

KW - Latin squares

KW - structured low-density parity-check codes

KW - trapping sets

UR - http://www.scopus.com/inward/record.url?scp=84858995475&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84858995475&partnerID=8YFLogxK

U2 - 10.1109/TIT.2011.2173733

DO - 10.1109/TIT.2011.2173733

M3 - Article

AN - SCOPUS:84858995475

VL - 58

SP - 2280

EP - 2302

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 4

M1 - 6169192

ER -