Improved Decoding of Binary and Non-Binary LDPC Codes by Probabilistic Shuffled Belief Propagation

Low-density parity-check (LDPC) codes have proved to be very powerful channel coding schemes with a broad range of applications. However, as maximum-likelihood decoding is utterly complex, suboptimal decoders have to be employed. One of the most popular decoding algorithms of LDPC codes is belief propagation (BP) decoding. In this paper, we present a novel scheduling for belief propagation decoding of LDPC codes. The new approach combines probabilistic scheduling with the known shuffled and check-shuffled serial scheduling algorithms. The resulting probabilistic shuffled and probabilistic check-shuffled decoders show a superior performance in terms of residual bit error rate. The drawback is that the convergence speed is slightly decreased. However, the convergence is still faster than for the standard and probabilistic flooding algorithms. Furthermore, we have adapted the probabilistic flooding schedule and the proposed probabilistic shuffled schedule to the non-binary case. We show that the aforementioned effects on the binary decoder can similarly be observed when applying the different schedules to the decoding of LDPC codes over higher order Galois fields.