Ordered Shuffle-BP Decoding Based on the Loops of LDPC Code

Ryoma Sakai, Matsuo Arisa, Kazuhiko Yamaguchi

Yoshiyuki Satô, Gou Hosoya, Hirasawa Shigeichi

Vikram Arkalgud Chandrasetty, Syed Mahfuzul Aziz

Moritz Beermann, Laurent Schmalen, Peter Vary

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.

Ya’nan Fan, Yao Xiujuan

Shuffled-BP (SBP) decoding algorithm is a variable-node-based serial decoding algorithm, which converges faster than the original Belief-Propagation (BP) decoding algorithm. However, due to the semi-parallel processing, there is a decrease in terms of convergence speed and error performance. An Overlapped Shuffled-BP(OSBP) decoding algorithm is proposed to enhance further the performance of the Shuffled-BP algorithm. In this algorithm, more than one sub-decoders are used to execute simultaneously, every sub-decoder has different updating order from each other. Regarding each variable node, the most reliable messages are kept and used for the next iteration, thus a faster convergence can be provided. Both theoretical analysis and simulation results show that, compared with SBP algorithm, OSBP algorithm possesses a better error performance as well as a higher convergence speed and introduces no extra storage requirement. Moreover, the proposed algorithm is effective for both regular and irregular LDPC codes.

Tom Høholdt, JØrn Justesen