Sum-Product Decoding of BCH Codes

Toshiyuki SHOHON

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A    No.10    pp.2729-2736
Publication Date: 2008/10/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.10.2729
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Coding Theory
sum-product decoding,  BCH codes,  Tanner Graph,  cycles of length four,  soft-in soft-out,  

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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.