Binary linear multicast network coding on acyclic networks: Principles and applications in wireless communication networks

Conventional linear multicast can be constructed on any acyclic network by increasing the order of the finite field to a sufficiently large amount over which the multicast is defined. In this paper, we first discuss the reciprocal theorem of the conventional linear multicast and design a linear multicast on any give acyclic network with constant finite field by extending the multicast dimension and relaxing the constraint on the information storage. In particular, we propose the binary linear multicast network coding and the linear multicast with binary coefficients. With the proposed method, the computation complexity for network coding at the intermediate nodes can be significantly reduced; therefore cheap network nodes can be deployed in a large scale due to their low cost for wireless communications. In addition, some applications of the proposed binary linear multicast network coding in wireless communication networks are illustrated and validated.