Minimum-Set Min-Sum Decoding Algorithms for Non-Binary LDPC Codes

During the check node (CN) update, the elements of input message vectors are redundant for the output message vectors. Hence, in this paper, we exactly select from the input message vectors the elements, which really have contributions to the error-correction performance and constitute the minimum set for the CN update. With adoption of the forward and backward (FB) scheme, an adaptive minimum-set min-sum algorithm (AMSA) is proposed to reduce the computation complexity of the FB process. In order to concurrently update the output vectors belonging to the same CN, we present a parallel minimum-set min-sum algorithm (PMSA) with lower memory complexity than the AMSA. Compared with the min-sum algorithms, the two proposed minimum-set based algorithms introduce no error performance loss.