The Effect of Hexagonal Grid Topology on the Throughput Benefit of Network Coding

The performance benefit of network coding in multihop wireless networks highly depends on network topology. Often, most studies on performance benefit of network coding focus on a generic grid topology, one of the most natural candidate topologies. Considering that hexagonal grid topology supports an optimal 2D plane network, in this paper, we study the effect of network topology on the performance benefit of network coding based on the highly structured wireless network of hexagonal grid topology. Firstly, we derive a tighter upper bound on the throughput benefit of network coding in single regular hexagon of multihop wireless networks. Secondly, we define network intensity to characterize the effect induced by the basic unit of hexagonal grid topology and demonstrate that the throughput benefit reaches the upper bound 12/7 in single regular hexagon only if the network intensity is greater than or equal to the positive square root of 3 and less than 2.