A Novel LLR-BP Algorithm for LDPC Codes Based on Taylor Series and Least Squares

Abstract:

An effective log-likelihood-ratio-based belief propagation (LLR-BP) algorithm is proposed. It can reduce computational complexity of decoding algorithm for Low Density Parity Check (LDPC) codes. By using the Taylor series and least squares, high order multiplication based on the hyperbolic tangent (tanh) rule is converted to a first-order multiplication and addition after simplification. Moreover, all the logarithmic and exponential operations disappear without significant loss of the decoding performance. The simulation results show that the performance of the proposed scheme is similar to the general LLR-BP. In particular, we show that the modified algorithm with low complexity can achieve better BER than the other decoding algorithm in high signal-to-noise ratio region.

• Periodical: Applied Mechanics and Materials (Volumes 462-463)
• Pages: 193-197
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.462-463.193
• Online since: November 2013
• Authors: Xing Ru Zhang*, Jian Ping Li, Chao Shi Cai
• Keywords: LDPC, Least Square (LS), LLR-BP, Taylor Series

References

[1] R. G. Gallager, Low density parity check codes, IRE Trans. Inform. Theory, vol. IT-8, p.21–28, Jan. (1962).

DOI: 10.1109/tit.1962.1057683

[2] D. J. C. MacKay, Good error-correcting codes based on very sparse matrices, IEEE Trans. Inform. Theory, vol. 45, p.399–432, Mar. (1999).

DOI: 10.1109/18.748992

[3] Tanner, R. M, A recursive approach to low complexity codes, IEEE Trans. Inform. Theory, 1981, 27, (5), p.533– 547.

DOI: 10.1109/tit.1981.1056404

[4] S. Y. Chung, G. D. Forney, Jr, T. J. Richardson, and R. Urbanke. On the design of low-density parity-check codes within 0. 0045 dB of the Shannon limit，, IEEE Commun. Lett , vol. 5, pp.58-60, Feb. (2001).

DOI: 10.1109/4234.905935

[5] Zengyou Sun, Jin Zhang, Juan Du, Research of LDPC Decoding Based on LLR BP Algorithm, Cross Strait Quad-Regional Radio Science and Wireless Technology Conference (CSQRWC), vol. 2, 2011, p.889 – 892.

DOI: 10.1109/csqrwc.2011.6037098

[6] Laouini, N, Ben. Hadj. Slama, L, Bouallegue,A. Fast decoding of low density parity check codes, High Capacity Optical Networks and Enabling Technologies (HONET), 2012, pp: 052 – 056.

DOI: 10.1109/honet.2012.6421434

[7] J. Chen, A. Dholakia, E. Eleftheriou, M.P.C. Fossorier, Reduced complexity decoding of LDPC codes, IEEE Trans. Commun. USA, vol. 53, no. 8, pp.1288-1299, Aug. (2005).

DOI: 10.1109/tcomm.2005.852852

[8] Papaharalabos, S., Sweeney, P., Evans, B. G, Albertazzi, G. Vanelli-Coralli, A., and Corazza, G.E. Performance evaluation of a modified sum-product decoding algorithm for LDPC codes, Proc. 2nd Int. Symp. Wireless Commun. Systems (ISWCS), Siena, Italy, p.800–804, Sep. (2005).

DOI: 10.1109/iswcs.2005.1547819

[9] S. Howard, C. Schlegel, and V. Gaudet. A degree-matched check node approximation for LDPC decoding, In Proceedings of the IEEE intl. Symposium on Information Theory, ISIT, Adelaide, Australia, pp.4-9, (2005).

DOI: 10.1109/isit.2005.1523516

[10] A, Reza, Banihashemi, Amir,H., A. Mahmoud, S. Hamid, LLR Approximation for Wireless Channels Based onTaylor Series and its Application to BICM With LDPC Codes, Transactions, 2012, 60, (5). pp: 1226-1236.

DOI: 10.1109/tcomm.2012.030712.110142

[11] Ying Wang, Lei Xie, Huifang Chen, Kuang Wang, Improved Decoding Algorithm of Bit-Interleaved Coded Modulation for LDPC Code, IEEE Trans. Broadcasting. pp.103-109, Mar. (2010).

DOI: 10.1109/tbc.2009.2036950