Simple relaying strategies for half-duplex networks

We consider the diamond network where a source communicates with the destination through N non-interfering half-duplex relays. Using simple outer bounds on the capacity of the network, we show that simple relaying strategies having exactly two states and avoiding broadcast and multiple access communication can still achieve a significant constant fraction of the capacity of the 2 relay network, independent of the SNR values. The results are extended to the case of 3 relays for the special class of antisymmetric networks. We also study the structure of (approximately) optimal relaying strategies for such networks. Simulations show that optimal schedules have at most N+1 states, which we conjecture to be true in general. We prove the conjecture for N = 2 and in special cases for N = 3.