Physical-layer network coding and information combining for the multiple-access relay network

We propose a new linear physical-layer network coding and information combining scheme for the K-user fading multiple-access relay network (MARN), which consists of K users, one relay and one destination. The relay and the destination are connected via a rate-constraint backhaul link. In the proposed scheme, the K users transmit signals simultaneously. The relay and the destination receive the superimposed signals distorted by fading and noise. The relay reconstructs L linear combinations of the K users' messages, referred to as L network coded (NC) messages, and forwards them to the destination. The destination then attempts to recover all K users' messages by combining its received signals and the NC messages obtained from the relay. We develop an explicit expression on the selection of the coefficients of the NC messages at the relay that minimizes the end-to-end error probability at a high signal to noise ratio. We demonstrate that our proposed scheme outperforms the benchmark scheme significantly in an MARN.