Iterative hybrid decoding algorithm for LDPC codes based on attenuation factor

Abstract

An attenuated iterative reliability-based majority-logic (AIML) decoding algorithm for low-density parity-check (LDPC) codes is proposed, which pertains to hybrid decoding schemes. The algorithm is devised based on the orthogonal check-sums of one-step majority-logic (OSMLG) decoding algorithm in conjunction with certain of reliability measures of the received symbols. Computation of reliability measure of the syndrome sum is refined by introducing an attenuation factor. Simulation results show that, in binary-input additive white Gaussian noise (BI-AWGN) channel, the AIML decoding algorithm outperforms other popular iterative reliability-based majority-logic (IML) decoding algorithms with a slight increase in computational complexity. Within maximum iteration number of 5, the AIML algorithm can achieve almost identical error performance to sum-product algorithm (SPA). No error floor effect can be observed for the AIML algorithm down to the bit error rate (BER) of {\mathrm{10}}^{-\mathrm{8}}, while error floor appears for SPA around the BER of {\mathrm{10}}^{-\mathrm{7}} even with maximum iteration number of 100. Furthermore, the inherent feature of parallel procession for AIML algorithm enforces the decoding speed in contrast to those serial decoding schemes, such as weighted bit-flipping (WBF) algorithm.

Key words： attenuation factor; reliability-based; iterative; majority-logic; low-density parity-check (LDPC) codes

Acknowledgements

This work was supported by the Fundamental Research Funds for the Central Universities.

References

1 Gallager R G. Low-density parity-check codes. IRE Transactions on Information Theory, 1962, 8(1): 21-28

2 MacKay D J C, Neal R M. Near Shannon limit performance of low density parity check codes. Electronics Letters, 1996, 32(18): 1645-1646

3 MacKay D J C. Good error-correcting codes based on very sparse matrices. IEEE Transactions on Information Theory, 1999, 45(2): 399-431

4 Tanner R M. A recursive approach to low complexity codes. IEEE Transactions on Information Theory, 1981, 27(5): 533-547

5 Zhang J, Fossorier M P C. A modified weighted bit-flipping decoding of low density parity-check codes. IEEE Communications Letters, 2004, 8(3): 165-167

6 Mobini N, Banihashemi A H, Hemati S. A differential binary message-passing LDPC decoder. In: Proceedings of IEEE Global Telecommunications Conference. 2007, 3: 1561-1565

7 Chen C Y, Huang Q, Kang J Y, Zhang L, Lin S. A binary message-passing decoding algorithm for LDPC codes. In: Proceedings of the 47th Annual Allerton Conference on Communication, Control, and Computing. 2009, 424-430

8 Huang Q, Kang J Y, Zhang L, Lin S, Abdel-Ghaffar K. Two reliability-based iterative majority-logic decoding algorithms for LDPC codes. IEEE Transactions on Communications, 2009, 57(12): 3597-3606

9 Jiang M, Zhao C M, Shi Z H, . An improvement on the modified weighted bit flipping decoding algorithm for LDPC codes. IEEE Communications Letters, 2005, 9(9): 814-816

10 Guo F, Hanzo L. Reliability ratio based weighted bit-flipping decoding for LDPC codes. In: Proceedings of the 61st IEEE Vehicular Technology Conference. 2005, 1: 709-713

11 Dong G Q, Li Y N, Xie N D, Zhang T, Liu H P. Candidate bit based bit-flipping decoding algorithm for LDPC codes. In: Proceedings of IEEE International Symposium on Information Theory. 2009, 2166-2168

12 Lee C H, Wolf W. Implementation-efficient reliability ratio based weighted bit-flipping decoding for LDPC codes. Electronics Letters, 2005, 41(13): 755-757

13 Chen J H, Fossorier M P C. Near optimum universal belief propagation based decoding of low-density parity check codes. IEEE Transactions on Communications, 2002, 50(3): 406-414

14 Wu X F, Ling C, Jiang M, Xu E Y, Zhao C M, You X H. New insights in weighted bit-flipping decoding. IEEE Transactions on Communications, 2009, 57(8): 2177-2180

15 Wu X F, Ling C, Jiang M, . Towards understanding weighted bit-flipping decoding. In: Proceedings of IEEE International Symposium on Information Theory. 2007, 1666-1670

16 Lin S, Costello D J. Error Control Coding: Fundamentals and Applications. 2nd ed. Upper Saddle River, NJ: Prentice Hall, 2004

17 Kou Y, Lin S, Fossorier M P C. Low density parity check codes based on finite geometries: A rediscovery and new results. IEEE Transactions on Information Theory, 2001, 47(7): 2711-2736

18 Proakis J G. Digital Communications. 5th ed. USA: McGraw-Hill Higher Education, 2008

19 Reed I S. A class of multiple-error-correcting codes and decoding scheme. IRE Transactions on Information Theory, 1954, 4(4): 38-49

20 Massey J L. Threshold Decoding. Cambridge, MA: MIT Press, 1963

21 MacKay D J C. Encyclopedia of Sparse Graph Codes. Available: http://www.inference.phy.cam.ac.uk/mackay/codes/data.html

22 Liu M H. Hybrid decoding for LDPC codes. Dissertation for the Master Degree. Beijing: Beijing Jiaotong University, 2010, 43-46 (in Chinese)