### Abstract

The parity-check matrix of a non-binary low-density parity-check (LDPC) code over GF(q) is constructed by assigning non-zero elements from GF(q) to the 1s in that of the corresponding binary LDPC code. In this paper, we provide a theorem that establishes a necessary and sufficient condition that a q-ary matrix constructed by assigning non-zero elements from GF(q) to the 1s in the parity-check matrix of a binary quasi-cyclic LDPC code must satisfy in order for its null-space to define a non-binary quasicyclic LDPC (NB-QC-LDPC) code over GF(q). We then propose a general scheme for constructing NB-QC-LDPC codes along with some other code construction schemes that might serve better for different design goals. We also demonstrate that NBQC-LDPC codes are very suitable for high-rate applications, e.g. applications in magnetic recording and storage systems and optical communication systems.

Original language | English (US) |
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Title of host publication | Proceedings of the 2009 ACM International Wireless Communications and Mobile Computing Conference, IWCMC 2009 |

Pages | 764-769 |

Number of pages | 6 |

DOIs | |

State | Published - Nov 30 2009 |

Event | 2009 ACM International Wireless Communications and Mobile Computing Conference, IWCMC 2009 - Leipzig, Germany Duration: Jun 21 2009 → Jun 24 2009 |

### Publication series

Name | Proceedings of the 2009 ACM International Wireless Communications and Mobile Computing Conference, IWCMC 2009 |
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### Other

Other | 2009 ACM International Wireless Communications and Mobile Computing Conference, IWCMC 2009 |
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Country | Germany |

City | Leipzig |

Period | 6/21/09 → 6/24/09 |

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### Keywords

- Low-density parity-check codes
- Non-binary quasi-cyclic codes

### ASJC Scopus subject areas

- Computer Networks and Communications
- Computer Science Applications
- Software

### Cite this

*Proceedings of the 2009 ACM International Wireless Communications and Mobile Computing Conference, IWCMC 2009*(pp. 764-769). (Proceedings of the 2009 ACM International Wireless Communications and Mobile Computing Conference, IWCMC 2009). https://doi.org/10.1145/1582379.1582545