Low-Complexity Compute-and-Forward Techniques for Multisource Multirelay Networks

Compute-and-forward (C&F) relaying in a multisource multirelay network is studied in this letter and two novel algorithms are proposed, addressing choice of integer matrix, taking into account the effect of singularity. The first algorithm assumes that there is no co-operation between the nodes for choosing proper integer vectors in the relay nodes; this method is referred to as “blind C&F” and an algorithm is proposed which guarantees that each relay chooses the best integer vector that contains information from at least m source nodes. In the second algorithm that is described as “partially coordinated C&F,” we assume that partial cooperation between the relay nodes and propose to exchange a single variable with which the relays are sorted for transmission. The performance of the proposed algorithm is nearly equivalent with optimal relaying, which requires significant overhead signaling.