Compute-and-forward on Compound Multiple Access Relay Channel

In this work, we study a Compound Multiple Access Relay Channel (C-MARC). The system is a simultaneous multicast network where all destinations are intended to receive and decode signals from all transmitters. Particularly, we focus on the model of two transmitters communicating, simultaneously, with two destinations with the help of a half-duplex relay. We extend and adapt the lattice-based compute-and-forward coding scheme to the model we study. This coding scheme is implemented at the relay and at the destinations through some modulo reduction operations. The relay computes one of the linear combinations and then forwards it, simultaneously to the destinations where the other linear combinations will be computed based on the direct transmissions. In this paper, we discuss the design criteria, and derive the allowed symmetric-rate. An optimization problem will then be formulated and solved through a Mixed Integer Quadratic Programming (MIQP) problem. The analysis shows that our coding scheme can offer substantial gain over standard relaying techniques such that amplify-and-forward and decode-and-forward for this model. We illustrate our results through some numerical examples.