采用基于GF（q）的LDPC编码实现带宽有效传输及编码设计

研究了AWGN信道条件下基于有限域GF(q)的非规则低密度奇偶校验编码与q进制结合实现带宽有效传输和编码优化方法。采用了Davey所提出的方法，为寻找基于GF(q)的多进制LDPC“好码”，可以选定校验矩阵的一组行重量参数，在一组关于校验矩阵重量参数的线形的约束条件下最小化一个非线性代价函数。使用该方法，一个比较重要的参数(平均列重量)将无法参加优化，这是因为行重量参数一经选定，平均列重也随之确定，因此不再将行重量参数固定，而是将行重参数的约束纳入优化约束条件，并引入复纯形法来解决所引出的非线性规划问题，从而保证列重量参数也参加优化。

Bandwidth efficient transmission of LDPC codes over GF(q) with optimal constructions

In this paper, the authors combine irregular LDPC codes over GF(q) and q-ary modulations for bandwidth efficient transmission over AWGN channel and consider the optimization of the codes. To find a good LDPC code over GF(q), based on the previous work by Davey, one may choose a row profile and minimize a non-linear objective function subject to a series of linear constraints about the column profile of the parity check matrix. One major drawback of this method is that an important parameter, the average column (row) weight, doesn't participate in the optimization since the average column weight is determined as soon as a row profile is given. We relax Davey's constraints of fixed row profile, using instead all the constraints about the row profile, the column profile and the average column weight and introduce the complex method to solve this non-linear programming problem. This ensures that the average column weight of the parity-check matrix participates in the optimization.