© The Institution of Engineering and Technology
A simple and efficient search method based on the coset concept is proposed to construct (3, L) quasi-cyclic low-density parity-check (QC-LDPC) codes without small cycles. Compared with the random search method, the chance to find large-girth codes is remarkably increased for the new method. Compared with Tanner's construction, the proposed method is much more flexible in the selection of row weight L. Some new codes are constructed with the shortest lengths compared with those constructed by the existing well-known methods. Simulation results show that the novel codes with moderate length perform well in the additive white Gaussian noise channel.
References
-
-
1)
-
30. Bocharova, I.E., Hug, F., Johannesson, R., et al: ‘Searching for voltage graph-based LDPC tailbiting codes with large girth’, IEEE Trans. Inf. Theory, 2012, 58, (4), pp. 2265–2279 (doi: 10.1109/TIT.2011.2176717).
-
2)
-
M. Fossorier
.
Quasi-cyclic low-density parity-check codes from circulant permutation matrices.
IEEE Trans. Inf. Theory
,
8 ,
1788 -
1793
-
3)
-
9. Zhang, J.-W., Li, C-X., Bao, J-R.: ‘A construction method of QC-LDPC codes without short cycles’. 4th Int. Conf. on Multimedia Information Networking and Security, Nanjing, China, November 2012, pp. 138–141.
-
4)
-
33. Kim, S., No, J.-S., Chung, H., Shin, D.-J.: ‘On the girth of Tanner (3, 5) quasi-cyclic LDPC codes’, IEEE Trans. Inf. Theory, 2006, 52, (4), pp. 1739–1744 (doi: 10.1109/TIT.2006.871060).
-
5)
-
6. Dai, Y.-M., Yan, Z.-Y., Chen, N.: ‘Optimal overlapped message passing decoding of quasi-cyclic LDPC codes’, IEEE Trans. Very Large Scale Integr. (VLSI) Syst., 2008, 16, pp. 565–578 (doi: 10.1109/TVLSI.2008.917540).
-
6)
-
1. Vasic, B., Pedagani, K., Ivkovic, M.: ‘High-rate girth-eight low-density parity-check codes on rectangular integer lattices’, IEEE Trans. Commun., 2004, 52, pp. 1248–1252 (doi: 10.1109/TCOMM.2004.833037).
-
7)
-
8. Gholami, M., Mostafaiee, F.S.: ‘On the girth of Tanner (3, 7) quasi-cyclic LDPC codes’, Trans. Comb., 2012, 1, pp. 1–16.
-
8)
-
14. O'Sullivan, M.E.: ‘Algebraic construction of sparse matrices with large girth’, IEEE Trans. Inf. Theory, 2006, 52, (2), pp. 718–727 (doi: 10.1109/TIT.2005.862120).
-
9)
-
7. Djordjevic, I.B., Arabaci, M., Minkov, L.L.: ‘Next generation FEC for high-capacity communication in optical transport networks’, J. Lightwave Technol., 2009, 27, pp. 3518–3530 (doi: 10.1109/JLT.2009.2022044).
-
10)
-
11. Zhang, G.-H., Sun, R., Wang, X.-M.: ‘Deterministic construction of girth-eight (3, L) QC-LDPC codes from quadratic function’, Electron. Lett., 2013, 49, pp. 600–602 (doi: 10.1049/el.2013.0320).
-
11)
-
5. Wu, X.-F., You, X.-H., Zhao, C.-M.: ‘A necessary and sufficient condition for determining the girth of quasi-cyclic LDPC codes’, IEEE Trans. Commun., 2008, 56, pp. 854–867 (doi: 10.1109/TCOMM.2008.060362).
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