### 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 - 2009 |

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

### Other

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

Country | Germany |

City | Leipzig |

Period | 6/21/09 → 6/24/09 |

### Fingerprint

### 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) https://doi.org/10.1145/1582379.1582545

**Regular non-binary quasi-cyclic LDPC codes for high-rate applications.** / Arabaci, Murat; Djordjevic, Ivan B; Saunders, Ross; Marcoccia, Roberto M.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 2009 ACM International Wireless Communications and Mobile Computing Conference, IWCMC 2009.*pp. 764-769, 2009 ACM International Wireless Communications and Mobile Computing Conference, IWCMC 2009, Leipzig, Germany, 6/21/09. https://doi.org/10.1145/1582379.1582545

}

TY - GEN

T1 - Regular non-binary quasi-cyclic LDPC codes for high-rate applications

AU - Arabaci, Murat

AU - Djordjevic, Ivan B

AU - Saunders, Ross

AU - Marcoccia, Roberto M.

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - Low-density parity-check codes

KW - Non-binary quasi-cyclic codes

UR - http://www.scopus.com/inward/record.url?scp=70450277330&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70450277330&partnerID=8YFLogxK

U2 - 10.1145/1582379.1582545

DO - 10.1145/1582379.1582545

M3 - Conference contribution

SN - 9781605585697

SP - 764

EP - 769

BT - Proceedings of the 2009 ACM International Wireless Communications and Mobile Computing Conference, IWCMC 2009

ER -