从π-旋转LDPC码到Q-矩阵LDPC码的演进

Evolvement from the π-rotation LDPC codes to the Q-matrix LDPC codes

介绍了基于π 旋转矩阵的低密度奇偶校验码(LDPC码)的构造方法,对π 旋转矩阵进行了研究和改造,对其约束条件进行加强,在此基础上定义了Q 矩阵,并提出Q 矩阵LDPC码的构造方法。Q 矩阵是约束满足问题的解,具有快速搜索算法,并能用循环移位的方法获得Q 矩阵集。利用Q 矩阵能快速灵活地构造不含4线循环的大型稀疏奇偶校验矩阵,从而生成LDPC码。提出的编码器设计基本思想是按照有利于LDPC码的构成及其电路设计的方式将奇偶校验矩阵H分解成两个子矩阵,通过对H的分解与重构运算直接构成码字。由于不需生成矩阵G,使LDPC码编码器的实现代价大幅度的降低。

A structuring method of low-density parity-check codes (LDPC) based on π-rotation matrix is introduced. The π-rotation matrix is studied and improved and its constraint conditions are enhanced. Accordingly the Q-matrix is defined and corresponding Q-matrix LDPC codes are presented. A Q-matrix is a solution of a constraint satisfaction problem, which features a fast searching algorithm and can form the Q-matrix set by cyclic shift. It is possible to construct quickly and effectively large sparse parity-check matrix without 4-line cycle by exploiting Q-matrixes, consequently to generate LDPC codes. The basic designing idea of encoder is to decompose the parity-check matrix H into two systematic sub-matrixes for the convenience of construction and circuit design of the LDPC code, thus directly creating LDPC codeword. As there is no need to form generation matrix G, the cost of implementing LDPC encoder is largely reduced.