Recently, Low Density Parity-Check (LDPC) codes based on Affine Permutation Matrices (APM) drew lots of attention. Compared with the Quasi-Cyclic LDPC (QC-LDPC) codes, these kinds of codes have some advantages. APM-LDPC codes obtain lower cycle-distributions, minimum hamming distance and greater girth. This paper explains the importance of cyclic distribution by comparing APM-LDPC codes with QC-LDPC codes. Then a particular form of APM-LDPC codes is proposed and researched. The new codes can low down the cycle-distribution to larger extent. In the following research, an effective method, which constructs the new codes with fixed girth, is proposed. Simulations show that the construction method is reasonable and effective. The transmission performances are better than the traditional methods, as well. Finally, the implementation and verification are carried out on FPGA.

中文翻译：

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基于仿射置换矩阵的低密度奇偶校验码

最近，基于仿射置换矩阵（APM）的低密度奇偶校验（LDPC）码引起了很多关注。与准循环LDPC（QC-LDPC）码相比，这类码具有一定的优势。APM-LDPC码获得更低的循环分布、最小的汉明距离和更大的周长。本文通过比较 APM-LDPC 码和 QC-LDPC 码来解释循环分布的重要性。然后提出并研究了一种特殊形式的APM-LDPC码。新代码可以在更大程度上降低循环分布。在接下来的研究中，提出了一种有效的方法，即构造具有固定周长的新代码。仿真表明该施工方法合理有效。传输性能也优于传统方法。最后，