Matrix analysis
Maximum-likelihood decoding of Reed-Solomon codes is NP-hard
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Low-complexity soft decoding algorithms for reed-solomon codes
Low-complexity soft decoding algorithms for reed-solomon codes
Modern Coding Theory
Algebraic soft-decision decoding of Reed-Solomon codes
IEEE Transactions on Information Theory
Iterative Soft-Input Soft-Output Decoding of Reed–Solomon Codes by Adapting the Parity-Check Matrix
IEEE Transactions on Information Theory
On iterative soft-decision decoding of linear binary block codes and product codes
IEEE Journal on Selected Areas in Communications
Iterative algebraic soft-decision list decoding of Reed-Solomon codes
IEEE Journal on Selected Areas in Communications
IEEE/ACM Transactions on Networking (TON)
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A new iterative soft decision decoding method for Reed-Solomon (RS) codes is proposed. This method is based on bit level belief propagation (BP) decoding. In order to make BP decoding effective for RS codes, we use an extended binary parity check matrix with a lower density and reduced number of 4-cycles compared to the original binary parity check matrix of the code. In our proposed method, we take advantage of the cyclic structure of RS codes. Based on this property, we can apply the belief propagation algorithm on any cyclically shifted version of the received symbols with the same binary parity check matrix. For each shifted version of received symbols, the geometry of the factor graph will change and deterministic errors can be avoided. Our method results in considerable performance improvement of RS codes compared to hard decision decoding. The performance is also superior to some popular soft decision decoding methods.