On the Multicast Capacity of Wireless Ad Hoc Networks with Network Coding

In this paper, we study the contribution of network coding (NC) in improving the multicast capacity of random wireless ad hoc networks when nodes are endowed with multi-packet transmission (MPT) and multi-packet reception (MPR) capabilities. We show that a per session throughput capacity of ${\Theta}$(nT$^3$(n)) can be achieved as a tight bound when each session contains a constant number of sinks where n is the total number of nodes and T(n) is the transmission range. Surprisingly, an identical order capacity can be achieved when nodes have only MPR and MPT capabilities. This result proves that NC does not contribute to the order capacity of multicast traffic in wireless ad hoc networks when MPR and MPT are used in the network. The result is in sharp contrast to the general belief (conjecture) that NC improves the order capacity of multicast. Furthermore, if the communication range is selected to guarantee the connectivity in the network, i.e., ${\Omega}$($\sqrt{log\;n/n}$)=T(n) = O(log log n / log n), then the combination of MPR and MPT achieves a throughput capacity of ${\Theta}$(log$^{\frac{3}{2}}$ n/$\sqrt{n}$) which provides an order capacity gain of ${\Theta}$(log$^2$ n) compared to the point-to-point multicast capacity with the same number of destinations.