A Method for Constructing Parity-Check Matrices of Quasi-Cyclic LDPC Codes Over GF(q)
- 56 Downloads
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.
Keywords:LDPC code parity-check matrix iterative decoding threshold Tanner graph cycle Galois field
The research was carried out at Skoltech and supported by the Russian Science Foundation (project no. 18-19-00673).
- 1.R. M. Tanner, “On quasi-cyclic repeat-accumulate codes,” in Proc. 37th Allerton Conf. Commun., Contr., Comput., Monticello, IL, Sept. 22–24, 1999 (Allerton House, 1999), pp. 249–259.Google Scholar
- 5.J. Thorpe, “Low-density parity-check (LDPC) codes constructed from protographs,” JPL, IPN Progress Rep. 42, 154 (2003).Google Scholar
- 10.H. Wymeersch, H. Steendam, and M. Moeneclaey, “Log-domain decoding of LDPC codes over GF(q),” in Proc. IEEE Int. Conf. on Communications,Paris, June 20–24, 2004 (IEEE, Piscataway, 2004), pp. 772–776.Google Scholar
- 11.L. Barnault and D. Declercq, “Fast decoding algorithm for LDPC over GF(2q),” in Proc. 2003 Inf. Theory Workshop, Paris, France, Mar. 2003 (IEEE, Piscataway, 2003), pp. 70–73.Google Scholar
- 13.G. Liva and M. Chiani, “Protograph LDPC codes design based on EXIT analysis,” in Proc. IEEE Global Telecommun. Conf. (GLOBECOM 2007), Washington, DC, Nov. 26–30, 2007 (IEEE, New York, 2007), pp. 3250–3254.Google Scholar
- 15.A. Bazarsky, N. Presman, and S. Litsyn, “Design of non-binary quasi-cyclic LDPC codes by ACE optimization,” in Proc. IEEE Inf. Theory Workshop, Sevilla, Spain, 2013 (IEEE, New York, 2013).Google Scholar
- 17.X. Hu, E. Eleftheriou, and D. Arnold, “Irregular progressive edge-growth (PEG) tanner graphs,” in Proc. ISIT 2002, Lausanne, Switzerland, June 30–July 5, 2002 (IEEE, New York, 2002).Google Scholar
- 20.D. J. C. MacKay and M. C. Davey, “Evaluation of Gallager codes for short block length and high rate applications,” in Codes, Systems, and Graphical Models, Minneapolis, MN, 1999, Ed. by B. Marcus and J. Rosenthal (Springer-Verlag, New York, 2001), pp. 113–130.Google Scholar