Title: Graph Permutation Selection for Decoding of Error Correction Codes using Self-Attention. Abstract: Error correction codes are an integral part of communication applications and boost the reliability of transmission. The optimal decoding of transmitted codewords is the maximum likelihood rule, which is NP-hard. For practical realizations, suboptimal decoding algorithms are employed; however, the lack of theoretical insights currently impedes the exploitation of the full potential of these algorithms. One key insight is the choice of permutation in permutation decoding. We present a data-driven framework for permutation selection combining domain knowledge with machine learning concepts such as node embedding and self-attention. Significant and consistent improvements in the bit error rate are shown for the simulated Bose Chaudhuri Hocquenghem (BCH) code as compared to the baseline decoders. To the best of our knowledge, this work is the first to leverage the benefits of self-attention networks in physical layer communication systems.
