In order to solve the problem of multi-source multi-sink multicast network coding, an algorithm for computing achievable information rate region and an approach for constructing linear network coding scheme were proposed. Based on the previous studies, the multi-source multi-sink multicast network coding problem was transformed into a specific single-source multicast network coding scenario with a constraint at the source node. By theoretical analyses and formula derivation, the constraint relationship among the multicast rate of source nodes was found out. Then a multi-objective optimization model was constructed to describe the boundary of achievable information rate region. Two methods were presented for solving this model. One was the enumeration method, the other was multi-objective optimization method based on genetic algorithm. The achievable information rate region could be derived from Pareto boundary of the multi-objective optimization model. After assigning the multicast rate of source nodes, the linear network coding scheme could be constructed by figuring out the single-source multicast network coding scenario with a constraint. The simulation results show that the proposed methods can find out the boundary of achievable information rate region including integral points and construct linear network coding scheme.

Based on single-source multicast network coding, in order to explore the relationship between multicast rate and the number of minimal needed coding nodes, by employing the technique of generation and extension of linear network coding, theoretical analysis and formula derivation of the relationship were given. It is concluded that the number of the minimal needed coding nodes monotonously increases with the increasing of multicast rate. A multi-objective optimization model was constructed, which accurately described the quantitative relationship between them. For the sake of solving this model, a search strategy was derived to search all feasible coding schemes. By combining the search strategy with NSGA-II, an algorithm for solving this model was presented. In the case of being required to consider the tradeoff between them, the solution of the model is the basis of choice for determining network coding scheme. The proposed algorithm not only can search whole Pareto set, but also search part Pareto set related with certain feasible multicast rate region given by user with less search cost. The simulation results verify the conclusion of theoretical analysis, and indicate that the proposed algorithm is feasible and efficient.