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Permutation decoding gained recent interest as it can exploit the symmetriesof a code in a parallel fashion. Moreover, it has been shown that by viewingpermuted polar codes as polar subcodes, the set of usable permutations inpermutation decoding can be increased. We extend this idea to pre-transformedpolar codes, such as cyclic redundancy check (CRC)-aided polar codes, whichpreviously could not be decoded using permutations due to their lack ofautomorphisms. Using belief propagation (BP)-based subdecoders, we showcase aperformance close to CRC-aided SCL (CA-SCL) decoding. The proposed algorithmoutperforms the previously best performing iterative CRC-aided beliefpropagation list (CA-BPL) decoder both in error-rate performance and decodinglatency.

A Polar Subcode Approach to Belief Propagation List Decoding