Abstract: Generalized distributed fountain codes (GDFC) were proposed as a distributed fountain coding scheme for multi-source single-relay networks. The degree distributions of the relay and sources are optimized by a two-step optimization method using linear and nonlinear programs, respectively. However, the optimization method is with high complexity, and the optimization results depend on the selection of the initial degree distribution. To address this problem, a novel simplified optimization method based on nonlinear program is presented. The proposed method only needs to optimize the degree distributions of the sources and only a simplified one-step optimization is used. Thus, the selection of the initial degree distribution of the sources can be avoided, and the performance can be improved. Compared with the two-step optimization method, the proposed one-step optimization method improves the efficiency and reduces the complexity. Simulations show that the proposed method can enhance the robustness and reliability of the optimization. Simulation results also verify that the bit error rate (BER) can be reduced and the decoding performance of GDFC can be improved.