The throughput order of multicast traffics with physical-layer network coding in random wireless ad hoc networks

This paper attempts to address the effectiveness of physical-layer network coding (PNC) on the throughput improvement for multi-hop multicast in random wireless ad hoc networks (WAHNs). We prove that the per session throughput order with PNC is tightly bounded as Θ((n(√m)R(n))^-1) if m = O(R^-2(n)), where n is the total number of nodes, R(n) is the communication range, and m is the number of destinations for each multicast session. We also show that per session throughput order with PNC is tight bounded as Θ(n^-1), when m = Ω(R^-2 (n)). The results of this paper imply that PNC cannot improve the throughput order of multicast in random WAHNs, which is different from the intuition that PNC may improve the throughput order as it allows simultaneous signal access and combination.