Fast Decoding of the p-Ary First-Order Reed-Muller Codes Based On Jacket Transform
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Doubly generalized LDPC codes over the AWGN channel
IEEE Transactions on Communications
Subcodes of Reed-Solomon codes suitable for soft decoding
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Grassmannian packings from operator Reed-Muller codes
IEEE Transactions on Information Theory
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A maximum a posteriori (MAP) probability decoder of a block code minimizes the probability of error for each transmitted symbol separately. The standard way of implementing MAP decoding of a linear code is the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm, which is based on a trellis representation of the code. The complexity of the BCJR algorithm for the first-order Reed-Muller (RM-1) codes and Hamming codes is proportional to n2, where n is the code's length. In this correspondence, we present new MAP decoding algorithms for binary and nonbinary RM-1 and Hamming codes. The proposed algorithms have complexities proportional to q2n logqn, where q is the alphabet size. In particular, for the binary codes this yields complexity of order n log n.