Sum-Product Decoding of BCH Codes
Pages 2729 - 2736
Abstract
This paper proposes methods to improve soft-input and soft-output decoding performance of BCH codes by sum-product algorithm (SPA). A method to remove cycles of length four (RmFC) in the Tanner graph has been proposed. However, the RmFC can not realize good decoding performance for BCH codes which have more than one error correcting capability. To overcome this problem, this paper proposes two methods. One is to use a parity check matrix of the echelon canonical form as the starting check matrix of RmFC. The other is to use a parity check matrix that is concatenation (ConC) of multiple parity check matrices. For BCH(31,11,11) code, SPA with ConC realizes Eb/No 3.7 dB better at bit error rate 10-5 than the original SPA, and 3.1 dB better than the SPA with only RmFC.
References
[1]
D. Chase, “A class of algorithms for decoding block codes with channel measurement information,” IEEE Trans. Inf. Theory, vol.IT-18, no.1, pp.170–182, 1972.
[2]
R.M. Pyndiah, “Near-optimum decoding of product codes: Block turbo codes,” IEEE Trans. Commun., vol.46, no.8, pp.1003–1010, Aug. 1998.
[3]
K. Kasai, T. Shibuya, and K. Sakaniwa, “A code-equivalent transformation removing cycles of length four in Tanner graphs,” IEICE Technical Report, IT2004-42, 2004.
[4]
S. Sankaranarayanan, “Iterative decoding of linear block codes: A parity-check orthogonalization approach,” IEEE Trans. Inf. Theory, vol.51, no.9, pp.3347–3353, Sept. 2005.
[5]
J. Chen and P.C. Fossorier, “Near optimum universal belief propagation based decoding of low-density parity check codes,” IEEE Trans. Commun., vol.50, no.3, pp.406–414, March 2002.
[6]
Y. Li and W.E. Ryan, “Bit-reliability mapping in LDPC-coded modulation systems,” IEEE Commun. Lett., vol.9, no.1, Jan. 2005.
[7]
J. Chen, A. Dholakia, E. Eleftheriou, M.P.C. Fossorier, and X.-Y. Hu, “Reduced-complexity decoding of LDPC Codes,” IEEE Trans. Commun., vol.53, no.8, pp.1288–1299, Aug. 2005.
[8]
T. Shohon, Y. Soutome, and H. Ogiwara, “Simple computation method of soft value for iterative decoding for product code composed of linear block code,” IEICE Trans. Fundamentals, vol.E82-A, no.10, pp.2199–2203, Oct. 1999.
[9]
W.W. Peterson and E.J. Weldon, Jr., Error-correction codes, Second ed., pp.283–299, MIT Press, 1972.
[10]
G.D. Forney, Jr. and M.D. Trott, “The dynamics of group codes: State spaces, trellis diagrams, and canonical encoders,” IEEE Trans. Inf. Theory, vol.39, no.9, pp.1491–1513, Sept. 1993.
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Copyright © Copyright © 2008 The Institute of Electronics, Information and Communication Engineers.
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Oxford University Press, Inc.
United States
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Published: 01 October 2008
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