Capacity scaling of wireless networks with complex field network coding

Network coding in wired networks has been shown to achieve considerable throughput gains relative to traditional routing networks. While the ergodic capacity of wireless multihop networks is unknown, the scaling of capacity with the number of nodes (n) has recently received increasing attention. While existing works mainly focus on networks with n source-destination pairs, this paper deals with capacity scaling in any-to-any wireless links, where each node communicates with all other nodes. Complex field network coding (CFNC) is adopted at the physical layer to allow n nodes exchanging information with simultaneous transmissions from multiple sources. A hierarchical CFNC-based scheme is developed and shown to achieve asymptotically (as n→∞) optimal quadratic capacity scaling in a dense network, where the area is fixed and the density of nodes increases. This is possible by dividing the network into many clusters, with each cluster sub-divided into many sub-clusters, hierarchically.