Information theory of wireless networks

An information theory of wireless networks is one of the grand challenges of the field. But 30 years of sustained effort in network information theory has produced exact capacity results only for the simplest of networks. We present two recent approaches to approximate the capacity of general networks in regimes which are meaningful in the wireless context. The first approach focuses on the interference-limited regime where the background noise is small compared to the received signals. The noisy wireless network is approximated by a natural deterministic one for which the capacity can be determined exactly with a max-flow min-cut interpretation. Moreover, the capacity-achieving scheme on this deterministic network translates naturally to a scheme which is near-optimal for the original noisy network. The second approaches focuses on the large-network regime and develops scaling laws on how the information theory capacity scales with the number of nodes. We will show how such scaling laws can be used to categorize networks into bandwidth-limited and power limited regimes, in analogy with those of point-to-point links.