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

Abstract: A novel permuted fast successive-cancellation list decoding algorithm with fast Hadamard transform (FHT-FSCL) is presented. The proposed decoder initializes $L$ $(L\ge1)$ 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 $10^{-4}$.