On the Application of Nested Lattice Coding in Wireless Networks
Lattice coding has emerged as a fundamental theoretical tool in the Information Theory of Gaussian networks. Lattice codes under lattice decoding achieve the capacity of the Gaussian channel, achieve the diversity-multiplexing tradeoff of quasi-static MIMO point to point channels, have been used to construct ``practical'' Costa Coding and Wyner-Ziv coding schemes and, more recently, have been widely applied to relay networks (compute and forward scheme) and interference channels (signal-level interference alignment).In this talk, we review a number of recent applications of nested lattice coding. In particular, we consider simple multi-access and broadcast relay networks modeling the uplink and the downlink of Distributed Antenna Systems (DAS) with a capacity constrained digital backhaul and centralized decoding (for the uplink) and precoding (for the downlink). We introduce ``Reverse Compute and Forward'' as a new downlink precoding scheme for DAS that explicitly takes into account the limited backhaul capacity. Then, we consider a class of network-coded two-user cognitive interference channel where one sender has the two messages and the other sender has a rank-deficient linear combination of the two messages, and show that lattice coding can achieve 2 degrees of freedom and in general a significant improvement of the generalized degrees of freedom, while it is known that the standard cognitive case does not improve the degrees of freedom. We consider also applications to a 2x2x2 MIMO network and to a diamond relay network. In the first case, lattice coding yields the best known degrees of freedom and a sizable finite SNR performance, while in the second case we show how to achieve full duplex relaying with half duplex relays.