The throughput order of ad hoc networks employing network coding and broadcasting

Gupta and Kumar established that the per node throughput of ad hoe networks with multi-pair unicast traffic scales as lambda(n) = Theta(1/root n log n), thus indicating that network performance does not scale well with an increasing number of nodes. However, the model of Gupta and Kumar did not allow for the possibility of network coding and broadcasting, and recent work has suggested that such techniques have the potential to greatly improve network throughput. Here, for multiple unicast flows in a random topology under the protocol communication model of Gupta and Kumar [1], we show that for arbitrary network coding and broadcasting in a two-dimensional random topology that the throughput scales as lambda(n) = Theta(1/nr(n)), where n is the total number of nodes and r(n) is the transmission radius. When r(n) is set to ensure connectivity, lambda(n) = Theta(1/root n log n), which is of the same order as the lower bound for the throughput without network coding and broadcasting; in other words, network coding and broadcasting at most provides a constant factor improvement in the throughput. This result is also extended to one-dimensional and three-dimensional random deployment topologies, where it is shown that lambda(n) = Theta(1/n) for the one-dimensional topology and lambda(n) = Theta((1)/3 root n log (2)n) for three-dimensional networks.