围长至少为8的QC-LDPC码的新构造:一种显式框架

Novel Constructions of QC-LDPC Codes with Girth at Least Eight:An Explicit Framework

构造围长较大的校验矩阵,是提高二进制和多进制QC-LDPC码译码性能的一种有效手段.本文提出一种不需要借助于任何计算机搜索步骤,能够直接构造出围长至少为8的QC-LDPC码的显式构造框架.该框架所构造的QC-LDPC码不仅满足围长至少为8的条件,而且还具有循环置换矩阵(CPM)尺寸可以连续变化的优点.该框架可以分为两个步骤:第一步是在无穷大CPM尺寸条件下利用确定性方法构造一个围长至少为8的校验矩阵;第二步是根据本文新发现的一个围长性质,从该校验矩阵的移位矩阵直接精确地计算出CPM尺寸连续变化的紧致下界.

Enabling the parity-check matrices to have a large girth is an efficient method to improve the decoding perfor- mance for many binary and non-binary QC-LDPC codes. A new explicit framework to construct QC-LDPC codes with girth at least eight is proposed, without any computer search procedures. The QC-LDPC codes constructed by the framework not only have a girth at least eight,but also possess an advantage of consecutive cyclic permutation matrix （CPM） sizes. The framework includes two steps：first, a parity-check matrix is explicitly constructed with a girth at least eight under an infinite CPM size;second, the tight low- er bound of consecutive CPM sizes is precisely calculated directly from the corresponding shift matrix of the parity-check matrix, by employing a new girth property discovered by this paper.