高误码率下LDPC稀疏校验矩阵重建

针对LDPC重建问题,提出了一种可直接重建LDPC稀疏校验矩阵的算法。首先,根据传统重建算法原理,详细分析了传统重建算法存在的缺陷以及缺陷存在的原因;其次,基于LDPC稀疏矩阵的特性,通过多次随机抽取码字中部分比特序列进行高斯消元,同时为了可靠实现抽取的比特序列能包含校验节点,基于一次抽取包含校验节点的概率,确定多次随机抽取的次数;最后,在误码条件下,基于疑似校验向量关系成立的统计特性和最小错误判决准则,实现稀疏校验向量的判定。仿真结果表明,所提算法在误码率为0.001的条件下,针对目前IEEE 802.11协议中大部分LDPC的重建率能达到95%以上,且噪声稳健性优于传统的重建算法,同时所提重建算法不仅不再需要对校验矩阵稀疏化处理,而且对于双对角线与非双对角线形式的校验矩阵都具有较好的通用性。

Reconstruction of sparse check matrix for LDPC at high bit error rate

In order to reconstruct the sparse check matrix of LDPC,a new algorithm which could directly reconstruct the LDPC was proposed.Firstly,according to the principle of the traditional reconstruction algorithm,the defects of the traditional algorithm and the reasons for the defects were analyzed in detail.Secondly,based on the characteristics of sparse matrix,some bit sequences in code words were randomly extracted for Gaussian elimination.At the same time,in order to reliably realize that the extracted bits sequence could contain parity check nodes,the multiple random variables were determined based on the probability of containing check nodes in one extraction.Finally,the statistical characteristics of LDPC under the suspected check vector was analyzed.Based on the minimum error decision rule,the sparse check vector was determined.The simulation results show that the rate of reconstruction of most LDPC in IEEE 802.11 protocol can reach more than 95%at BER of 0.001,and the noise robustness of the proposed method is better than that of the traditional algorithm.At the same time,the new algorithm not only does not need sparseness of parity check matrix,but also has the good performance for both diagonal and non-diagonal check matrix.