Research On Efficient Decoding Algorithms For Nonbinary LDPC Codes

Non-binary low-density parity-check (NB-LDPC) codes, at short and medium block lengths can achieve better error-correcting performance than their binary counterparts. But, currently proposed nonbinary decoding algorithms have very high complexity for high-throughput implementations, which is a significant barrier to practical realization. In this paper, we present three high efficient decoding algorithms for non-binary LDPC codes which have lower complexity and higher performance.First, we propose the objective driven search algorithm. In this algorithm, when we update the check node, firstly, we update the field element with the maximal check-to-variable message by the maximal variable-to-check message in each branch. Secondly, for the remaining field elements, we do not loop through all the combinations from the neighbor variable nodes, but to build available check-sum equation set for each of them. The process of building check-sum equation set is based on the maximum principle and absolute minimum principle. In order to reduce the loss by increasing the amount of information, we combine the two principles and the objective driven search algorithm.Secondly, vector error correct model for non-binary LDPC codes with faster convergence, better error performance and lower complexity is proposed. We show that it is possible to greatly reduce the computational complexity of the check node processing by applying objective driven search algorithm. Furthermore, this algorithm eliminates the error by adding compensation value. Simulation shows the outperforming performance compared with FFT-QSPA.Finally, we propose two dynamic scheduling algorithms named Q-VNRS (q-ary variable node reliability-based scheduling) and Q-VNMRS (q-ary variable node maximum reliability-based scheduling) for decoding non-binary LDPC codes. These algorithms use the advantages of non-binary LDPC codes with q-dimensional information vector for each node. Q-VNRS and Q-VNMRS calculate the difference of variable-to-check message values by the maximal and minor value in the variable node, while the VC-RBP (Variable-to-check residual belief propagation) for binary LDPC codes calculates the residual from the difference of variable-to-check message values before and after update. Therefore, if a message has a small difference, it means that the message is located in a part of the graph that has not yet converged. Therefore, propagating the message having the small difference first should speed up the process.