%0 Journal Article %1 geiselhart2021iterativeRM %A Geiselhart, Marvin %A Elkelesh, Ahmed %A Ebada, Moustafa %A Cammerer, Sebastian %A Brink, Stephan ten %D 2021 %K myown %T Iterative Reed-Muller Decoding %U http://arxiv.org/abs/2107.12613 %X Reed-Muller (RM) codes are known for their good maximum likelihood (ML) performance in the short block-length regime. Despite being one of the oldest classes of channel codes, finding a low complexity soft-input decoding scheme is still an open problem. In this work, we present a belief propagation (BP) decoding architecture for RM codes based on their rich automorphism group. The decoding algorithm can be seen as a generalization of multiple-bases belief propagation (MBBP) using polar BP as constituent decoders. We provide extensive error-rate performance simulations and compare our results to existing decoding schemes. We report a near-ML performance for the RM(3,7)-code (e.g., 0.05 dB away from the ML bound at BLER of $10^-4$) at a competitive computational cost. To the best of our knowledge, our proposed decoder achieves the best performance of all iterative RM decoders presented thus far.

@article{geiselhart2021iterativeRM, abstract = {Reed-Muller (RM) codes are known for their good maximum likelihood (ML) performance in the short block-length regime. Despite being one of the oldest classes of channel codes, finding a low complexity soft-input decoding scheme is still an open problem. In this work, we present a belief propagation (BP) decoding architecture for RM codes based on their rich automorphism group. The decoding algorithm can be seen as a generalization of multiple-bases belief propagation (MBBP) using polar BP as constituent decoders. We provide extensive error-rate performance simulations and compare our results to existing decoding schemes. We report a near-ML performance for the RM(3,7)-code (e.g., 0.05 dB away from the ML bound at BLER of $10^{-4}$) at a competitive computational cost. To the best of our knowledge, our proposed decoder achieves the best performance of all iterative RM decoders presented thus far.}, added-at = {2021-07-28T11:46:56.000+0200}, author = {Geiselhart, Marvin and Elkelesh, Ahmed and Ebada, Moustafa and Cammerer, Sebastian and Brink, Stephan ten}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/24edf65bbc1629796359c15ec13139766/mgeiselhart}, description = {[2107.12613] Iterative Reed-Muller Decoding}, interhash = {13308c6919f40bb901acd2603cf1d635}, intrahash = {4edf65bbc1629796359c15ec13139766}, keywords = {myown}, note = {cite arxiv:2107.12613 Comment: 5 pages, accepted for publication at the International Symposium on Topics in Coding 2021 (ISTC), Sep. 2021. Short version of arXiv:2012.07635}, timestamp = {2021-07-28T09:46:56.000+0200}, title = {Iterative Reed-Muller Decoding}, url = {http://arxiv.org/abs/2107.12613}, year = 2021 }