Decoding Reed-Muller Codes Using Minimum- Weight Parity Checks

Elia Santi, Christian Hager, Henry D. Pfister
2018 2018 IEEE International Symposium on Information Theory (ISIT)  
Reed-Muller (RM) codes exhibit good performance under maximum-likelihood (ML) decoding due to their highlysymmetric structure. In this paper, we explore the question of whether the code symmetry of RM codes can also be exploited to achieve near-ML performance in practice. The main idea is to apply iterative decoding to a highly-redundant paritycheck (PC) matrix that contains only the minimum-weight dual codewords as rows. As examples, we consider the peeling decoder for the binary erasure
more » ... l, linear-programming and belief propagation (BP) decoding for the binary-input additive white Gaussian noise channel, and bit-flipping and BP decoding for the binary symmetric channel. For short block lengths, it is shown that near-ML performance can indeed be achieved in many cases. We also propose a method to tailor the PC matrix to the received observation by selecting only a small fraction of useful minimum-weight PCs before decoding begins. This allows one to both improve performance and significantly reduce complexity compared to using the full set of minimum-weight PCs.
doi:10.1109/isit.2018.8437637 dblp:conf/isit/SantiHP18 fatcat:4kvseoxu6jhfxls7ud53vq5hzm