Characterization and Optimization of LDPC Codes for the 2-User Gaussian Multiple Access Channel

We address the problem of designing good LDPC codes for the Gaussian multiple access channel (MAC). The framework we choose is to design multiuser LDPC codes with joint belief propagation decoding on the joint graph of the 2-user case. Our main result compared to existing work is to express analytically EXIT functions of the multiuser decoder with two different approximations of the density evolution. This allows us to propose a very simple linear programming optimization for the complicated problem of LDPC code design with joint multiuser decoding. The stability condition for our case is derived and used in the optimization constraints. The codes that we obtain for the 2-user case are quite good for various rates, especially if we consider the very simple optimization procedure.