Cooperation / Contention - an Information Theoretic Perspective Syed A. Jafar University of California Irvine What is the optimal form of cooperation? How much does it help ? At what cost (overhead) ?

What is the Optimal form of Cooperation? To answer the question, we need to know the capacity of wireless networks. We know: Large network scaling laws [Gupta, Kumar ‘00,…, Ozgur, Johari, Leveque, Tse 08] 2 node interference channel capacity within one bit. [Etkin, Tse, Wang 07] For any no. of nodes, the capacity of wireless networks with accuracy approaching 100% as local noise at each node becomes small [Cadambe, Jafar 07, 08] –Regardless of the number of users, every user achieves half his interference-free rate over the same channel (Interference Alignment)

R1 R3 Interference Alignment: Everyone gets half the cake. T2 Propagation Delay T3 R2 T1

Capacity of Interference Networks As local noise becomes small, regardless of the number of interferers each user achieves half of the capacity he would achieve if there was NO interference. Optimal : innerbound = outerbound Random time-varying channels. No Propagation Delays. Any number of users. Any number of antennas. At high SNR, capacity higher than prior belief by 50%, 900% and 4900% for 3,20,100 users. Relays, Feedback, Cooperation do not help beyond o(log(SNR))

Contention (hurt) –Access divided like a cake. –K users, each gets 1/K of the cake. –Low overhead. Cooperation (help) –Nodes relay messages. –Hierarchical Cooperation, Network Coding, Mobile Relays. –Primarily helpful to counter propagation path loss (multihop). –Overhead can be significant. Neutral (do no harm) –Interference Alignment Everyone gets half of their interference free rate at high SNR. –Capacity Optimal at high SNR. –Primarily the solution to interference problem. –Global channel knowledge will constitute huge overhead. –Distributed algorithms based on channel reciprocity reduce overhead.

Conclusion New tools expected to lead to more accurate capacity characterizations –Deterministic Channel Models [Avestimehr, Diggavi, Tse] –Interference Alignment [Cadambe, Jafar] –Structured Codes [Nazer, Gastpar] –Generalized Degrees of Freedom [Etkin,Tse, Wang] Fundamental characterization of overhead seems more distant.