Compute-and-Forward: Optimization Over Multisource-Multirelay Networks

In this paper, we investigate a multisource multicast network with the aid of an arbitrary number of relays, where it is assumed that no direct link is available at each S-D pair. The aim is to find the fundamental limit on the maximal common multicast throughput of all source nodes if resource allocations are available. A transmission protocol employing the relaying strategy, i.e., compute-and-forward (CPF), is proposed. We also adjust the methods in the literature to obtain the integer network-constructed coefficient matrix (i.e., a naive method, a local optimal method, and a global optimal method) to fit the general topology with an arbitrary number of relays. Three transmission scenarios are addressed. The first scenario is delay-stringent transmission, where each message must be delivered within one slot. The second scenario is delay-tolerant transmission where no delay constraint is imposed. The associated optimization problems to maximize the short-and long-term common multicast throughputs are formulated and solved, and the optimal allocation of power and time slots are presented. The third case (a general N-slot-delay-tolerant scenario) is also discussed, and a suboptimal algorithm is presented. Performance comparisons show that the CPF strategy outperforms conventional decode-and-forward (DF) strategy. It is also shown in the simulation that with more relays, the CPF strategy performs even better due to the increased diversity. Finally, by simulation, it is observed that, with CPF, the N-slot-delay-constraint case can perform close to that of the delay-tolerant case in terms of throughput, given that N is relatively large.