The Ergodic Capacity of Interference Networks

We identify the role of equal strength interference links as bottlenecks on the ergodic sum capacity of a network. It is shown that even though there are K(K − 1) cross-links, only about K/2 disjoint and equal strength interference links suffice to determine the capacity of the network regardless of the strengths of the rest of the cross channels. This scenario is called a minimal bottleneck state. It is shown that ergodic interference alignment is capacity optimal for a network in a minimal bottleneck state. The results are applied to large networks. It is shown that large networks are close to bottleneck states with a high probability, so that ergodic interference alignment is close to optimal for large networks. Lastly some interesting examples are provided of parallel channels where separate coding is optimal.