Set Message-Passing Decoding Algorithms for Regular Non-Binary LDPC Codes

In the check node (CN) update of non-binary message-passing algorithms, each element of reliability vectors takes the same computational complexity. However, our analysis indicates that various elements in the same vector have various correct probabilities, thus have different contributions to error performance. In order to match computational complexity with correct probability, all elements in a vector are partitioned into different sets. For the extended min-sum (EMS) decoding, various strategies are applied for sets according to their correct probability. For the trellis-based EMS decoding, it is interesting that set partition only involves fixed paths, thus it does not need to search over the whole trellis of a CN. Complexity analysis and simulation results show that the proposed algorithms efficiently decode non-binary low-density parity-check codes, including ultra-sparse ones.