This paper proposes a new method of constructing compact fully-connected Quasi-Cyclic Low Density Parity Check (QC-LDPC) codes with girth g = 8, 10, and 12. The originality of the proposed method is to impose constraints on the exponent matrix P to reduce the search space drastically. For a targeted lifting degree of N, the first step of the method is to sieve the integer ring Z_N to make a particular sub-group with specific properties to construct the second column of P (the first column being filled with zeros). The remaining columns of P are determined recursively as multiples of the second column by adapting the sequentially multiplied column (SMC) method whereby a controlled greedy search is applied at each step. The codes constructed with the proposed semi-algebraic method show lengths that can be significantly shorter than their best counterparts in the literature.

翻译：本文提出了一种新方法,用Girth g = 8、10和12来构建连接齐全的“准-单元低密度对齐”代码(QC-LDPC),以Girth g = 8、10和12。拟议方法的原创性是对前列矩阵P施加限制,以大幅缩小搜索空间。对于N的定向提升程度,方法的第一步是筛选整形环+N,使具有特定特性的特定分组能够构建P第二列(第一列填零)。P的其余列通过调整每步采用受控贪婪搜索的相乘列方法,被确定为第二列的倍数。用拟议的半正数方法构建的代码显示长度可以大大短于文献中的最佳对应方的长度。