Cryptanalysis of the Sidelnikov Cryptosystem
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Error exponents for two soft-decision decoding algorithms of Reed-Muller codes
IEEE Transactions on Information Theory
Enhanced CDMA communications using compressed-sensing reconstruction methods
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
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Soft-decision decoding is considered for general Reed-Muller (RM) codes of length n and distance d used over a memoryless channel. A recursive decoding algorithm is designed and its decoding threshold is derived for long RM codes. The algorithm has complexity of order nlnn and corrects most error patterns of the Euclidean weight of order radicn/lnn, instead of the decoding threshold radicd/2 of the bounded distance decoding. Also, for long RM codes of fixed rate R, the new algorithm increases 4/pi times the decoding threshold of its hard-decision counterpart