A Method for Constructing Parity-Check Matrices of Quasi-Cyclic LDPC Codes Over GF(q)

Abstract

An algorithm for constructing parity-check matrices of non-binary quasi-cyclic low-density parity-check (NB QC-LDPC) codes is proposed. The algorithm finds short cycles in the base matrix and tries to eliminate them by selecting the circulants and the elements of GF(q). The algorithm tries to eliminate the cycles with the smallest number edges going outside the cycle. The efficiency of the algorithm is demonstrated by means of simulations. In order to explain the simulation results we also derive upper bounds on the minimum distance of NB QC-LDPC codes.

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Notes

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    The weight of a circulant is a weight of its first row.

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ACKNOWLEDGMENTS

The research was carried out at Skoltech and supported by the Russian Science Foundation (project no. 18-19-00673).

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Correspondence to S. A. Kruglik or V. S. Potapova or A. A. Frolov.

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Kruglik, S.A., Potapova, V.S. & Frolov, A.A. A Method for Constructing Parity-Check Matrices of Quasi-Cyclic LDPC Codes Over GF(q). J. Commun. Technol. Electron. 63, 1524–1529 (2018). https://doi.org/10.1134/S1064226918120112

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Keywords:

  • LDPC code
  • parity-check matrix
  • iterative decoding threshold
  • Tanner graph
  • cycle
  • Galois field