Geometrical bounds on the efficiency of wireless network coding

This paper explores wireless network coding both in case of deterministic and random point patterns. Using the Boolean connectivity model we provide upper bounds for the maximum encoding number, i.e., the number of packets that can be combined such that the corresponding receivers are able to decode. For the models studied, this upper bound is of order √N, where N denotes the (mean) number of neighbours. Our simulations show that the √N law is applicable to small-sized networks as well. Moreover, achievable encoding numbers are provided for grid-like networks where we obtain the multiplicative constants analytically. Building on the above results, we provide an analytic expression for the upper bound of the efficiency of wireless network coding. The conveyed message is that it is favourable to reduce computational complexity by relying only on small encoding numbers, for example, XORing only pairs, as the resulting throughput loss is typically small.