Good LDPC codes over GF(q) for bandwidth efficient transmission

In this paper, we 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 (1998, 1999), one may choose a row profile and minimize a nonlinear 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, does not 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 nonlinear programming problem. This ensures that the average column weight of the parity-check matrix participates in the optimization.