The capacity of wireless interference networks is one of the most important open problems of network information theory. Much progress has been made on this problem within the past decade. However, the initial focus has been on divergent extremes: where channel knowledge is available either with infinite precision or entirely absent; where the interference is either too strong or too weak; where channels are either perfectly constant or independently varying. Where previous studies have focused on extreme scenarios to arrive at radically divergent conclusions, this research reconciles the divergent extremes by resolving incompatibilities wherever they exist and exploiting synergies everywhere possible.
The research is comprised of three main components ? exploring progressively, the full range of partial channel knowledge, channel strengths, and channel coherence patterns. The stepping stones for the three thrusts include recent advances in topological interference management, the optimality of treating interference as noise, and blind interference alignment. The final critical ingredient of this research is a breakthrough in robust outer bounds, called the Aligned Image Sets (AIS) approach ? a novel combinatorial argument that bounds the relative size of the images cast by a set of codewords at different receivers based on the amount of channel knowledge available to the transmitters.
The research combines the theoretical pursuit of capacity limits with the practical concern for robustness. Understanding the capabilities of wireless communication networks in robust settings is essential for the industry, the academia, the government agencies and the society in general to have realistic expectations from the networks of the future.
