Information Theory of Networks: A Deterministic Approach

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Claude Shannon's point-to-point information theory is a basis for the design of all modern day communication systems, ranging from cellular communications, cable and DSL modems, statellite communications, compact disks, etc. Extending the theory from point-to-point communication to an entire network of communicating nodes is a holy grail of the communication field. It is expected that such an information theory of networks would have a significant impact for applications such as wireless and sensor networks. Yet, despite significant effort in the past 40 years, only isolated cases have been solved and there is still limited understanding of central issues such as interference, cooperation, broadcast and distributed compression of correlated information.This research advocates a new general approach to attack network information theory problems. The new approach involves three steps: 1) approximate the noisy network with an appropriately chosen deterministic model which focuses on the interaction between the various signals rather than the noise; 2) analyze the analytically simpler deterministic model; 3) translate the insight into finding approximately optimal strategy for the original noisy network with guaranteed performance bound. Significant progress on several canonical long-standing open problems shows the power of the approach: 1) capacity region of the two-user Gaussian interference channel to within 1 bit/s/Hz per user; 2) capacity of the Gaussian (single-node) relay channel to within 1 bit/s/Hz; 3) capacity of the Gaussian relay network with arbitrary number of relays to within constant gap independent of the SNR's of the links; 4) rate region of the Gaussian multiple description problem to within a constant gap independent of the target distortions of the users.