Network Coding Does Not Change the Multicast throughput Order of Wireless Ad Hoc Networks

We demonstrate that the gain attained by network coding (NC) on the multicast capacity of random wireless ad hoc networks is bounded by a constant factor. We consider a network with n nodes distributed uniformly in a unit square, with each node acting as a source for independent information to be sent to a multicast group consisting of m randomly chosen destinations. We show that, under the protocol model, the per- session capacity in the presence of arbitrary NC has a tight bound of Theta (1/radic(mnlog(n))) when m = O(n/(log(n))) and Theta(1/n) when m = Omega(n/(log(n))). Our result follows from the fact that prior work has shown that the same order bounds are achievable with pure routing based only on traditional store-and-forward methods.