Bandwidth efficient transmission of LDPC codes over GF(q) with optimal constructions
Xiangming Li · Journal of Chongqing University of Posts and Telecommunications · 2005
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.