AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Efficient encoding of QC-LDPC codes related to cyclic MDS codes
IEEE Journal on Selected Areas in Communications - Special issue on capaciyy approaching codes
Two bit-flipping decoding algorithms for low-density parity-check codes
IEEE Transactions on Communications
A low complexity iterative technique for soft decision decoding of reed-solomon codes
ICC'09 Proceedings of the 2009 IEEE international conference on Communications
Multiple-bases belief-propagation decoding of high-density cyclic codes
IEEE Transactions on Communications
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Iterative decoding methods have gained interest, initiated by the results of the so-called “turbo” codes. The theoretical description of this decoding, however, seems to be difficult. Therefore, we study the iterative decoding of block codes. First, we discuss the iterative decoding algorithms developed by Gallager (1962), Battail et al. (1979), and Hagenauer et al. (1996). Based on their results, we propose a decoding algorithm which only uses parity check vectors of minimum weight. We give the relation of this iterative decoding to one-step majority-logic decoding, and interpret it as gradient optimization. It is shown that the used parity check set defines the region where the iterative decoding decides on a particular codeword. We make plausible that, in almost all cases, the iterative decoding converges to a codeword after some iterations. We derive a computationally efficient implementation using the minimal trellis representing the used parity check set. Simulations illustrate that our algorithm gives results close to soft decision maximum likelihood (SDML) decoding for many code classes like BCH codes. Reed-Muller codes, quadratic residue codes, double circulant codes, and cyclic finite geometry codes. We also present simulation results for product codes and parallel concatenated codes based on block codes