Resource allocation for multiple access relay channel with a compute-and-forward relay

In this work¹, we study a multiaccess relay channel (MARC). The system consists of two transmitters communicating with a destination with the help of a half-duplex relay. We extend and adapt the recently proposed lattice-based compute-and-forward coding scheme to the model we study. This coding scheme can be seen as a form of some network-coding that is implemented at the relay through modulo-reduction. In this scheme, the destination decodes two linear equations with integer coefficients that relate the transmitted symbols at different computational rates. First, we discuss the design criteria, and derive the allowed computation rate. Then, we optimally allocate the different parameters by solving a series of geometric programs using successive convex approximation methods. The analysis shows that our coding scheme can offer substantial gain over the standard amplify-and-forward and decode-and-forward for this model. We illustrate our results through some numerical examples.