Reconstruction of linear block code parity-check matrix based on fault-tolerant Gaussian elimination

Aiming at the problem of poor fault-tolerant performance in the reconstruction of the parity-check matrix of linear block codes, a parity-check matrix reconstruction algorithm based on fault-tolerant Gaussian elimination was proposed. Firstly, partial bits of codewords were randomly sampled multiple times to construct incomplete codewords. The reliability was calculated based on the mean and minimum of the absolute values of the bit log-likelihood ratios, so as to screen out high-reliability incomplete code groups. Secondly, for the partially incorrect states of the basis of the incomplete code groups, the fault-tolerant Gaussian elimination algorithm was used to solve the corresponding suspected parity-check vectors, and then the true parity-check vectors were determined and restored from them. Finally, according to whether the codeword bits could pass through the known parity-check vectors, the absolute values of the bit log-likelihood ratios were updated to further improve the bit reliability, bringing gains for the next random sampling of partial bits. The simulation results showed that, under the same identification conditions, the reconstruction rate of the proposed algorithm is higher than that of the existing algorithms. For the LDPC(648,324) code under the IEEE802.11n protocol, the existing algorithms fail when the bit error rate reaches 0.005 5, while the reconstruction rate of the proposed algorithm for the parity-check matrix still reaches over 98% when the bit error rate is 0.008.