@article{12233,
  abstract     = {A novel recursive list decoding (RLD) algorithm for Reed-Muller (RM) codes based on successive permutations (SP) of the codeword is presented. A low-complexity SP scheme applied to a subset of the symmetry group of RM codes is first proposed to carefully select a good codeword permutation on the fly. Then, the proposed SP technique is integrated into an improved RLD algorithm that initializes different decoding paths with random codeword permutations, which are sampled from the full symmetry group of RM codes. Finally, efficient latency and complexity reduction schemes are introduced that virtually preserve the error-correction performance of the proposed decoder. Simulation results demonstrate that at the target frame error rate of 10−3 for the RM code of length 256 with 163 information bits, the proposed decoder reduces 6% of the computational complexity and 22% of the decoding latency of the state-of-the-art semi-parallel simplified successive-cancellation decoder with fast Hadamard transform (SSC-FHT) that uses 96 permutations from the full symmetry group of RM codes, while relatively maintaining the error-correction performance and memory consumption of the semi-parallel permuted SSC-FHT decoder.},
  author       = {Doan, Nghia and Hashemi, Seyyed Ali and Mondelli, Marco and Gross, Warren J.},
  issn         = {1558-0857},
  journal      = {IEEE Transactions on Communications},
  number       = {11},
  pages        = {7134--7145},
  publisher    = {Institute of Electrical and Electronics Engineers},
  title        = {{Decoding Reed-Muller codes with successive codeword permutations}},
  doi          = {10.1109/tcomm.2022.3211101},
  volume       = {70},
  year         = {2022},
}

@article{6739,
  abstract     = {We explore the relationship between polar and RM codes and we describe a coding scheme which improves upon the performance of the standard polar code at practical block lengths. Our starting point is the experimental observation that RM codes have a smaller error probability than polar codes under MAP decoding. This motivates us to introduce a family of codes that “interpolates” between RM and polar codes, call this family C inter = {C α : α ∈ [0, 1j}, where C α|α=1 is the original polar code, and C α|α=0 is an RM code. Based on numerical observations, we remark that the error probability under MAP decoding is an increasing function of α. MAP decoding has in general exponential complexity, but empirically the performance of polar codes at finite block lengths is boosted by moving along the family Cinter even under low-complexity decoding schemes such as, for instance, belief propagation or successive cancellation list decoder. We demonstrate the performance gain via numerical simulations for transmission over the erasure channel as well as the Gaussian channel.},
  author       = {Mondelli, Marco and Hassani, Hamed and Urbanke, Rudiger},
  issn         = {0090-6778},
  journal      = {IEEE Transactions on Communications},
  number       = {9},
  pages        = {3084--3091},
  publisher    = {IEEE},
  title        = {{From polar to Reed-Muller codes: A technique to improve the finite-length performance}},
  doi          = {10.1109/tcomm.2014.2345069},
  volume       = {62},
  year         = {2014},
}