Estimation of Two-Dimensional Correction Factors for Min-Sum Decoding of Regular LDPC Code

Ahmed A. Hamad

Department of Electrical Engineering, University of Babylon, Babel, Iraq.

DOI: 10.4236/wet.2013.44027                

Abstract

In this paper, two-dimensional (2-D) correction scheme is proposed to improve the performance of conventional Min-Sum (MS) decoding of regular low density parity check codes. The adopted algorithm to obtain the correction factors is simply based on estimating the mean square difference (MSD) between the transmitted codeword and the posteriori information of both bit and check node that produced at the MS decoder. Semi-practical tests using software-defined radio (SDR) and specific code simulations show that the proposed quasi-optimal algorithm provides a comparable error performance as Sum-Product (SP) decoding while requiring less complexity.

Keywords

LDPC Code; Sum-Product; Min-Sum; 2-D Correction Factors; Software-Defined Radio (SDR)

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	R. G. Gallager, “Low-Density Parity Check Codes,” IRE Transactions on Information Theory, Vol. 8, No. 1, 1962, pp. 21-28.http://dx.doi.org/10.1109/TIT.1962.1057683
[2]	IEEE 802.11n, “Wireless LAN Medium Access Control and Physical Layer Specifications: Enhancement for Higher Throughput,” IEEE P802.11n/D1.0, 2006.
[3]	IEEE 802.16e, “Air Interface for Fixed and Mobile Broadband Wireless Access Systems,” IEEE P802.16e/D12 Draft, 2005.
[4]	European Telecommunications Standards Institude (ETSI), “Digital Video Broadcasting (DVB) Second Generation Framing Structure for Broadband Satellite Applications,” EN 302 307 v1.1.1, 2005.
[5]	N. Wiberg, “Codes and Decoding on General Graphs,” Ph. D. Thesis, Linkoping University, Linkoping, 1996.
[6]	M. P. C. Fossorier, M. Mihaljevic and H. Imai, “Reduced Complexity Iterative Decoding of Low-Density Parity Check Codes Based on Belief Propagation,” IEEE Transactions on Communications, Vol. 47, No. 5, 1999, pp. 673-680.
[7]	J. Chen and M. P. Fossorier, “Near Optimum Universal Belief Propagation Based Decoding of Low Density Parity Check Codes,” IEEE Transactions on Communications, Vol. 50, No. 3, 2002, pp. 406-414. http://dx.doi.org/10.1109/26.990903
[8]	J. Zhang, M. Fossorier, D. Gu and J. Zhang, “Two-Dimensional Correction for Min-Sum Decoding of Irregular LDPC Codes,” IEEE Communications Letters, Vol. 10, No. 3, 2006, pp. 180-182.
[9]	V. Savin, “Self-Corrected Min-Sum Decoding of LDPC Codes,” ISIT 2008. IEEE International Symposium on information Theory, 2008. ISIT 2008, Toronto, 6-11 July 2008, pp. 146-150. http://dx.doi.org/10.1109/ISIT.2008.4594965
[10]	H. Wei, J. G. Huang and F. F. Wu, “A Modified MinSum Algorithm for Low-Density Parity-Check Codes,” 2010 IEEE International Conference on Wireless Communications, Networking and Information Security (WCNIS), Beijing, 25-27 June 2010, pp. 449-451.
[11]	X. F. Wu, Y. Song, L. Cui, M. Jiang and Ch. Zhao, “Adaptive-Normalized Min-Sum Algorithm,” 2010 2nd International Conference on Future Computer and Communication (ICFCC), Wuhan, 21-24 May 2010, pp.V2-661V2-663.
[12]	A. A. Hamad, “Performance Enhancement of SOVA Based Decoder in SCCC and PCCC Schemes,” Scientific Research Magazine, Wireless Engineering and Technology, Vol. 4, No. 1, 2013, pp. 40-45. http://dx.doi.org/10.4236/wet.2013.41006
[13]	T. J. Richardson and R. L. Urbanke, “Efficient Encoding of Low-Density Parity-Check Codes,” IEEE Transactions on Information Theory, Vol. 47, No. 2, 2001, Article ID: 638456.
[14]	D. J. C. MacKay, “Good Error-Correcting Codes Based on Very Sparse Matrices,” IEEE Transactions on Information Theory, Vol. 45, No. 2, 1999, pp. 399-431. http://dx.doi.org/10.1109/18.748992
[15]	T. H. Shepertycki, “Telemetry Error Measurements Using Pseudo-Random Signals,” IEEE Transactions on Space Electronics and Telemetry, Vol. 10, No. 3, 1964, pp. 111-115. http://dx.doi.org/10.1109/TSET.1964.4335603