New results in network information theory: scaling laws and optimal operational modes for wireless networks

We present new results in network information theory. We show that when path loss attenuation is high, the transport capacity of a network with n² nodes in a square of side n is O(n²) bit-meters/second. Since this capacity can be achieved by multi-hop operation in many situations, it proves that multi-hop with all interference regarded as noise, and full decoding after each hop, is the order optimal operational mode under high attenuation. However, under small attenuation, long range action can be best. Interference cancellation is useful as is coherent cooperation among nodes. The network´s transport capacity can grow like O(n^θ) for 2<θ<4.