An algebraic polyphase approach to wireless network coding

Network coding has been shown to improve throughput, minimize delay and economize the energy requirements in wireless networks. This paper presents an algebraic polyphase approach to the wireless linear network coding problem. By modeling wireless nodes as consisting of linear periodic time varying filters, the model incorporates realistic constraints including omni directionality of transmissions, half-duplex operation and interference effects. A rank criterion is introduced, which together with the transmission constraints, constitutes the necessary and sufficient conditions for the existence of a wireless network code.