Successive-Cancellation Decoding of Reed-Muller Codes With Fast Hadamard Transform

A novel permuted fast successive-cancellation list decoding algorithm with fast Hadamard transform (FHT-FSCL) is presented. The proposed decoder initializes
$L$

$(L\geq 1)$
active decoding paths with
$L$
random codeword permutations sampled from the full symmetry group of the codes. The path extension in the permutation domain is carried out until the first constituent RM code of order 1 is visited. Conventional path extension of the successive-cancellation list decoder is then utilized in the information bit domain. The simulation results show that for a RM code of length 512 with 46 information bits, by running 20 parallel permuted FHT-FSCL decoders with
$L=4$
, we reduce 72% of the computational complexity, 22% of the decoding latency, and 84% of the memory consumption of the state-of-the-art simplified successive-cancellation decoder that uses 512 permutations sampled from the full symmetry group of the code, with similar error-correction performance at the target frame error rate of
$10^{-4}$
.