Performance Analysis of Wireless Network Coding via Percolation

In order to investigate the effect of network connectivity on the performance of wireless network coding, we introduce percolation theory to construct the system model of multi-hop wireless network for asymptotic connectivity. Concretely, we proposed a normalization algorithm for random network to layer the nodes of the largest connected component in multi-hop wireless network, and derived the theoretical conditions of percolation occurrence for the normalized hierarchical network of the largest connected component. Furthermore, according to the critical threshold of percolation phenomenon, we derived the performance of wireless network coding for the largest connected component. The mean delay and throughput were quantified in terms of network coding parameters such as coding window size, transmission radius, and node density. These conclusions clarify the effective performance of wireless network coding for random network, and will contribute to the evaluation of optimal performance of wireless network coding.