Sum-Product Decoding of BCH Codes

Haruo OGIWARA; Kyouhei SHIMAMURA; Toshiyuki SHOHON

doi:10.1093/ietfec/e91-a.10.2729

Sum-Product Decoding of BCH Codes

Haruo OGIWARA, Kyouhei SHIMAMURA, Toshiyuki SHOHON

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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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E91-A No.10 pp.2729-2736

Publication Date: 2008/10/01

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Online ISSN: 1745-1337

DOI: 10.1093/ietfec/e91-a.10.2729

Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)

Category: Coding Theory

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Haruo OGIWARA, Kyouhei SHIMAMURA, Toshiyuki SHOHON, "Sum-Product Decoding of BCH Codes" in IEICE TRANSACTIONS on Fundamentals, vol. E91-A, no. 10, pp. 2729-2736, October 2008, doi: 10.1093/ietfec/e91-a.10.2729.
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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e91-a.10.2729/_p

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@ARTICLE{e91-a_10_2729,
author={Haruo OGIWARA, Kyouhei SHIMAMURA, Toshiyuki SHOHON, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Sum-Product Decoding of BCH Codes},
year={2008},
volume={E91-A},
number={10},
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.},
keywords={},
doi={10.1093/ietfec/e91-a.10.2729},
ISSN={1745-1337},
month={October},}

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TY - JOUR
TI - Sum-Product Decoding of BCH Codes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2729
EP - 2736
AU - Haruo OGIWARA
AU - Kyouhei SHIMAMURA
AU - Toshiyuki SHOHON
PY - 2008
DO - 10.1093/ietfec/e91-a.10.2729
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E91-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2008
AB - 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.
ER -