Multicast Throughput Order of Network Coding in Wireless Ad-hoc Networks

We consider a network with n nodes distributed uniformly in a unit square. We show that, under the protocol model, when n_s = Ω (log(n)^1+α) out of the n nodes, each act as source of independent information for a multicast group consisting of m randomly chosen destinations, the per-session capacity in the presence of network coding (NC) has a tight bound of Θ(√n/n_s√mlog(n)) when m = O(n/log(n)) and Θ(1/n_s) when m = Ω(n/log(n)). In the case of the physical model, we consider n_s = n and show that the per-session capacity under the physical model has a tight bound of Θ(1/√mn) when m = O(n/(log(n))³), and Θ(1/n) when m = Ω(n/log(n)). Prior work has shown that these same order bounds are achievable utilizing only traditional store-and-forward methods. Consequently, our work implies that the network coding gain is bounded by a constant for all values of m. For the physical model we have an exception to the above conclusion when m is bounded by O(n/(log(n))³) and Ω(n/log(n)). In this range, the network coding gain is bounded by O((log(n))^1/2).