Multicast Capacity Gain and Routing Algorithm in Static Network with Network Coding

This paper studies the multicast capacity gain with network coding in static ad hoc wireless network. We consider $n$ nodes deployed in a square with $k$ nodes formulating multicast tree to employ network coding. In static unicast network, Liu et al. \cite{Liujunning},\cite{Liujunning2} have proved that the capacity gain with network coding is a constant without order change. In our work, we focus on the capacity gain with network coding in static multicast network, under the system model of Li \cite{xiangyang}'s. Firstly, we modify the routing algorithm of multicast model and propose that the multicast capacity bound in \cite{xiangyang} is just a theoretical result but not very tight in practical scenario. Then in static multicast transmission we calculate the probability of existing the butterfly model to employ network coding. Our result shows that there is no order change of the capacity. Finally, We prove that the bound of the capacity gain with network coding is $\frac{\tau}{\sqrt{2}}$, where $\tau=\frac{\sqrt{3}}{2}\cdot\tau(2)$, and $\tau(2)$ is a constant in dimension two, when network coding is applied to static multicast network.