Bp Decoding and Sgrand for Partially Permuted Factor Graphs of Polar Codes

Polar codes are provably capacity-achieving errorcorrecting codes suitable for error correction and source coding, constrained coding, and multiple access channels. Many decoding schemes have been proposed for Polar codes, including CRCaided successive cancellation list decoding (CA-SCL), known for its superior error-correcting performance. Belief propagation (BP) techniques have also been explored for decoding polar codes. BP decoding with partially permuted factor graphs (PPFG) exhibits good performance despite being inferior to CA-SCL decoding. Guess Random Additive Noise Decoding (GRAND) is a general decoding scheme for linear codes. Soft-GRAND (SGRAND) exhibits excellent performance for Polar codes despite its high time complexity. We introduce a novel decoding scheme that combines BP decoding with PPFG and SGRAND, advancing the state-of-the-art in Polar code decoding. Our proposed scheme, which fuses BP decoding with PPFG and SGRAND, demonstrates performance similar to that of CA-SCL decoding, representing a significant step forward in Polar code decoding.