Hybrid Decoding For Low-Density Parity-Check Codes

Hybrid decoding for low-density parity-check (LDPC) codes combines the features of hard-decision and soft-decision decoding. In hybrid decoding, reliability measures of hard-decision sequence are obtained from partial channel information. There is still a wide performance gap between hybrid decoding and soft-decision decoding, which has become an obstacle in those high-reliable communication systems. New hybrid decoding with better performance becomes a practical task for the research.Firstly, an improved weighted bit-flipping (WBF) decoding algorithm is proposed. In this algorithm, only the unsatisfied check-sums are used to get extrinsic information of received symbols, which reduces computational complexity. Simulation results show that error performances of improved WBF are almost identical to conventional WBF. Secondly, weighted one-step majority-logic (WMLG) decoding algorithm is deduced in the perspective of log-MAP decoding by using Jacobian logarithm. The conjecture that WMLG decoding approaches log-MAP decoding in terms of error performance is verified by simulation. On the basis of the essential of WMLG, an improved iterative MLG (IML) algorithm is proposed, and it processes the received sequence by adopting uneven quantization. Simulation result indicates that improved IML algorithm can obtain better error performance than IML. Finally, a weighted iterative OSMLG (WIO) algorithm is put forward. In WIO algorithm, computation of reliability measure of the check-sum is refined by introducing an attenuation factor and computation of extrinsic information is improved by precluding the information of symbol itself. The reliability measures of hard-decision symbols are updated in each iteration process. Simulation results show that WIO decoding algorithm outperforms all other popular hybrid decoding algorithms with a slight increase in computational complexity. Due to faster convergence speed of WIO decoding, error performances of LDPC codes decoded with WIO and SPA are almost identical with iterations no more than five. In compared with SPA, no error floor effect can be observed for WIO algorithm in high SNR region. The algorithm is robust in terms of attenuation factor. For implementation reason, attenuation factor can be chosen to be 0.5.