Network coded non-binary LDGM codes based on lattices for a multi-access relay system

In this paper, we propose a novel network coded non-binary low-density generator matrix (LDGM) code structure for a multi-access relay system, where multiple sources transmit lattice signals to a destination with the help of a relay. Specifically, we first develop a network coded non-binary LDGM code structure by jointly considering lattice-signal transmissions at the sources and the relay. Then we derive the achievable computation rate (ACR) for the proposed system and on that basis optimize the key parameters in the proposed structure to maximize the ACR. Furthermore, we optimize the network coded non-binary LDGM codes based on lattices to approach the ACR. Simulation results show that the optimal setting of the parameters is consistent with that obtained from our analysis and the proposed code structure outperforms the designed reference scheme.