Quasi-Cyclic Low-Density Parity-Check Codes With Girth Larger Than $12$
Quasi-Cyclic Low-Density Parity-Check Codes With Girth Larger Than $12$
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发表时间：
2007
影响因子：
2.5
通讯作者：
Sunghwan Kim;Jong-Seon No;Habong Chung;Dong-joon Shin
中科院分区：
文献类型：
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作者：
Sunghwan Kim;Jong-Seon No;Habong Chung;Dong-joon Shin
准循环(QC)低密度奇偶校验(LDPC)码可以看作是具有循环置换矩阵(或循环数)的原始码。在这个对应中，我们发现了QC LDPC码原图的所有子图模式都有长度为2i，i=6，7，8，9，10的必然圈，即无论循环数的移位值如何，总是存在的圈。还推导出如果原图的围长为2g，则其原图代码不可能有长度小于6g的必然圈。基于这些子图模式，我们提出了新的原始图的组合构造方法，其原始码的围长可以大于或等于14或18。我们还提出了保证围长14的QC-LDPC码的循环移位值分配规则。
A quasi-cyclic (QC) low-density parity-check (LDPC) code can be viewed as the protograph code with circulant permutation matrices (or circulants). In this correspondence, we find all the subgraph patterns of protographs of QC LDPC codes having inevitable cycles of length 2i, i = 6, 7, 8, 9,10, i.e., the cycles that always exist regardless of the shift values of circulants. It is also derived that if the girth of the protograph is 2g, g > 2, its protograph code cannot have the inevitable cycles of length smaller than 6g. Based on these subgraph patterns, we propose new combinatorial construction methods of the protographs, whose protograph codes can have girth larger than or equal to 14 or 18. We also propose a couple of shift value assigning rules for circulants of a QC LDPC code guaranteeing the girth 14.