The Optimization Of Decoding Algorithms For Non-binary LDPC Codes

Low density parity check (LDPC) codes is one of the channel codes which is by far closest to Shannon limit and is the main alternative of error correction codes in the next generation of broadband mobile communication system. Non-binary LDPC codes have a better performance than binary counterparts at short and medium block lengths, but the higher decoding complexity greatly limits the application of non-binary LDPC codes. Thus, reducing the decoding complexity becomes a focus of research in decoding algorithm for Non-binary LDPC codes. To get better tradeoff between performance and complexity of decoding, we propose four optimized decoding algorithms.Firstly, the reliability-ratio-based weighted symbol-flipping (RRWSF) decoding algorithm is proposed. Taking into account that the check is violated owing to any symbol in the check equation, the RRWSF decoding algorithm introduces a new symbol metrics which is the ratio of the reliability of symbol and the sum of all reliabilities of symbols which participate in the same check. As the new metric doesn’t separate the reliability of symbol and information from the check equations, it is unnecessary to obtain the optimal weighting factor through a large number of computer simulations. Simulation results show that RRWSF decoding algorithm not only reduces the decoding complexity, but also improves the decoding performance compared with WSF decoding algorithm.Secondly, the check-node-reliability-based serial belief propagation decoding algorithm is proposed. We define reliability for each check node and update information in the order which is based on its value. Since the check node which has lower reliability is updated preferentially, CRSBP decoding algorithm has faster convergence than traditional serial scheduling decoding algorithms. Simulation results show that CRSBP algorithm achieves about0.1dB coding gain over CSBP algorithm at the symbol error rate of10-2.Finally, the variable-node-probability-difference-based scheduling (Q-VNPDS) decoding algorithm and its improved version are proposed. Both of the algorithms are dynamic scheduling algorithms extended from binary field to finite field GF(q). In the Q-VNPDS decoding algorithm, we firstly calculate q absolute values of difference between the probability in the current iteration and the probability in previous iteration, wherein the maximum is treated as the metric of the variable node. These nodes connected to the variable node which has the worst convergence because of its maximum metric should be updated. The second decoding algorithm is the improved Q-VNPDS for reducing the decoding complexity. In the second algorithm, we should judge the maximum probabilities of variable nodes around two iterations first in order to select the variable nodes which should be calculate measures. If the corresponding field elements are identical, the variable node is deleted. Otherwise the variable node is reserved. Only the reserved nodes’ metrics need to be calculated. This step can reduce the amount of calculation. Then we can find the maximum probability of every variable node and the corresponding field element in current iteration. The next step is to find the probability of the variable node taking same field element in previous iteration, and then to calculate the absolute value of difference between the above two probabilities and assign it as the variable node metric. Simulation results show that these two decoding algorithms achieve about0.4dB performance gain over traditional flooding scheduling algorithm at the symbol error rate of10-2. The improved Q-VNPDS algorithm is0.2dB worse than the Q-VNPDS algorithm at the symbol error rate of10-3.