Abstract—Network coding in wired networks has been shown to achieve considerable throughput gains relative to traditional routing networks. For wireless multihop networks however, the ergodic capacity is unknown. In this context, 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-toany 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. As n increases, a hierarchical CFNC-based scheme is developed and shown to achieve asymptotically 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. As a result, information is transmitted on multi-input multi-output based multiple access channels and broadcast channels. When generalized to extended networks, where the density of nodes is fixed and the area increases linearly with n, the hierarchical CFNC scheme is shown to scale as n3−α/2 for a path loss exponent α ≥ 2, which is asymptotically optimal when α < 3.

Index Terms—Capacity scaling, hierarchical transmission, complex field network coding, multi-input multi-output (MIMO), multiple access channel (MAC), broadcast channel
(BC).

Cite:Tairan Wang and Georgios B. Giannakis, "Capacity Scaling of Wireless Networks with Complex Field Network Coding," Journal of Communications, vol. 4, no.11, pp.830-840 , 2009. Doi: 10.4304/jcm.4.11.830-840