  Error correction codes are an integral part of communication applications,
boosting the reliability of transmission. The optimal decoding of transmitted
codewords is the maximum likelihood rule, which is NP-hard due to the curse of
dimensionality. For practical realizations, sub-optimal decoding algorithms are
employed; yet limited theoretical insights prevent one from exploiting the full
potential of these algorithms. One such 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 introduced for all simulated codes, over the baseline
decoders. To the best of the authors' knowledge, this work is the first to
leverage the benefits of the neural Transformer networks in physical layer
communication systems.
