The effect of hexagonal grid topology on wireless communication networks based on network coding

Network coding has emerged as a promising technology that can provide significant improvements in the performance of wireless communication networks. Inspired by the recent advances in complex networks, we herein study the effect of topology structure on the performance benefit of network coding based on a highly structured wireless communication network with hexagonal grid topology. We propose a new concept called 'network intensity', namely γ to characterize the property of hexagonal grid topology. We first derive a value of 12/7 for the upper bound on performance benefit in a single regular hexagon network. This value holds only if the network intensity is in the case of 3 γ<2. Based on the results in a single regular hexagon network, we then derive a value of 16/7 for the upper bound on performance benefit in a general hexagonal grid network only if the network intensity is in the case of 1 γ<3. Furthermore, a comparative analysis demonstrates that the network intensity affects the performance benefit of network coding in terms of the interference and the coding number. These findings will contribute to the design of network topology and the analysis of the bound on the performance benefit of network coding in wireless communication networks.