On network coding in wireless ad-hoc networks

Network coding has been proven to be an effective way to achieve the maximum flow capacity in a multicast network, which is bounded by the famous maximum-flow minimum-cut theorem. This technique is specially fit for some new types of network, e.g., ad-hoc, sensor network etc. In order to reduce the cost and complexity of network coding, rather than carrying out encoding at all the nodes along the routes of traffic flow, it is better to find out the nodes that need encoding, and perform the coding algorithm at these nodes only, so that the number of encoding nodes are as few as possible. Fragouli et al. (2004) presented a method to get the encoding nodes by subtree decomposition. In this paper, we take a random graph as the model of wireless ad-hoc multicast network, and apply a modified Ford-Fulkerson algorithm to obtain the maximum flow and encoding nodes in an undirected graph. Its correctness can be proven in theory. Furthermore, simulations are done in different conditions to get some meaningful results of this scheme. We also investigate the statistical properties of encoding nodes and maximum flow in ad-hoc multicast networks by random graph theory. We showed that the number of encoding nodes is approximately binomial-distributed, and as the size of the network tends to infinite, it is approximately a Poisson distribution