A multiple unicasts wireless network where multiple paths are available for each unicast is considered. To minimise the total network cost which is defined as the number of transmissions to support the given data flows of the network, general network coding (GNC) and active general network coding (AGNC) are employed. AGNC can exploit more network coding opportunities than GNC by allowing some additional information which is transmitted to recover the native flows from the network coded ones.
The overall network cost minimisation problem can be decomposed into two sub-problems: source traffic splitting which can be resolved by potential game theory and network coding traffic adjusting which can be resolved by project gradient algorithm. Simulation results demonstrate that both of AGNC and GNC outperform the conventional scheme which does not adopt network coding. In addition, Better performance can be achieved by AGNC in contrast with GNC.