中文摘要：

该文提出一种通过合理设置零矩阵构造可逆准循环低密度奇偶校验码（QC-LDPC）的方法，解决了传统QC-LDPC码校验矩阵不满秩及编码复杂度高的问题。将循环矩阵对应于有限域中的多项式，利用扩展的欧几里德算法构造可逆校验矩阵，克服了传统QC-LDPC码码率大于设计码率的问题。编码时先将校验矩阵分块，然后利用扩展欧几里德算法回溯求解循环矩阵的逆矩阵，显著降低了编码复杂度。EXIT图证明了译码器的收敛性。仿真表明短码时纠错性能优于随机LDPC码，适用于水声通信系统。另外，将可逆QC-LDPC码应用于ZP-OFDM系统的仿真表明QC-LDPC码能较大地提高水下通信系统的鲁棒性。

英文摘要：

A construction scheme of reversible Quasi Cyclic-Low Density Parity Check （QC-LDPC） codes is proposed by setting rationally zero matrices. This solves the problems of singular check matrix and high encoding complexity in conventional QC-LDPC codes. With circulant matrix corresponding to polynomial in finite fields, the scheme exploits the extended version of Euclid＇s algorithm to conquer the problem of QC-LDPC construction rate lager than design rate. Moreover, in the encoding process, first dividing the check matrix into blocks, and then the extended version of Euclid＇s algorithm is used to invert a circulant matrix, it results in dynamic complexity decrease. EXtrinsic Information Transfer （EXIT） chart implies the convergence of decoder. More simulations illustrate that the performance of the proposed construction structure is better than random LDPC when the code length is short, which is suitable for UnderWater Acoustic Communication （UWAC）. Finally, applying QC-LDPC to Zero Padding-Orthogonal Frequency Division Multiplexing （ZP-OFDM） for evaluating the performance in UWAC, extended simulation shows that the reversible QC-LDPC codes can dynamically improve the system robustness.