Abstract: QC-LDPC codes with slide rectangular window and quasi tri-diagonal structure are proposed, the more flexible code lengths and code rates of QC-LDPC codes are expanded by using slide rectangular window in the base check matrix, the degree distribution is optimized by the optimal diagonal method. The error floors of QC-LDPC codes are lower by using quasi tri-diagonal structure which appropriately selects the location of the third diagonal in the base check matrix to partly eliminate variable nodes of degree-2. Simulation results show the proposed QC-LDPC codes can not only flexibly expand the code lengths and code rates but also reduce the encoding complexity and improve the BER performance compared to quasi dual-diagonal structure in IEEE 802. 16e QC-LDPC codes, they are available and suitable for the adaptive transmission systems and hardware implementation.

Key words: Quasi-Cyclic Low-Density Parity-Check（QC-LDPC） codes, diagonal structure, degree distribution, encoding complexity

摘要： 针对IEEE 802.16e标准QC-LDPC码的码长和码率有限，及其采用的准双对角线结构包含大量度为2的变量节点导致较高错误平层的缺陷，提出一种基于滑动矩形窗和准三对角线结构的QC-LDPC码的快速编码算法，可以灵活地扩展码长和码率的范围，改善纠错性能，降低编码复杂度，适合于变速率的自适应传输系统。

关键词: 准循环低密度奇偶校验（QC-LDPC）码, 角线结构, 度分布, 编码复杂度