In a wireless network, interference between transmitters is usually viewed as highly undesirable and clever algorithms and protocols have been devised to avoid it. Collectively, these strategies transform the physical layer into a set of reliable bit pipes which can then be used seamlessly by higher layers in the protocol stack. Unfortunately, interference avoidance results in sharply decreasing rates as the number of users increases.
This talk proposes a new strategy, compute-and-forward, that exploits the interference property of the wireless channel to achieve higher end-to-end rates in a network. The key idea is that users should decode linear functions of the transmitted messages according to their observed channel coefficients rather than treating interference as noise. Structured codes (such linear codes or lattices) ensure that these linear combinations can be decoded reliably, often at far higher rates than the messages individually. Historically, codes with linear structure have been studied as a stepping stone to more practical constructions. More recently, several groups have shown that algebraic structure can significantly enhance performance in relay networks, interference channels, distributed source coding, distributed interference cancellation, and physical layer network coding, among others. Our recent work has employed compute-and-forward as a building block to develop efficient MIMO decoding architectures as well as determine the approximate sum capacity of a class of symmetric interference channels.