Soft Maximum Likelihood Decoding using GRAND

Abstract: Maximum Likelihood (ML) decoding of forward error correction codes is known to be optimally accurate, but is not used in practice as it proves too challenging to efficiently implement. Here we introduce a ML decoder called SGRAND, which is a development of a previously described hard detection ML decoder called GRAND, that fully avails of soft detection information and is suitable for use with any arbitrary high-rate, short-length block code. We assess SGRAND's performance on CRC-aided Polar (CA-Polar) codes, which will be used for all control channel communication in 5G NR, comparing its accuracy with CRC-Aided Successive Cancellation List decoding (CA-SCL), a state-of-the-art soft-information decoder specific to CA-Polar codes.