Capacities of Gaussian relay networks with accuracy within a constant number of bits

Abstract

We consider the capacities of wireless networks. In the first part of this work, a class of relay networks with orthogonal components (OC) is considered. In this class, we assume that outgoing channels at a node to its neighbors are orthogonal, while incoming signals from neighbors can interfere with each other. We are interested in the multicast capacity of these networks. As a subclass, we first focus on Gaussian relay networks with OC and find an achievable rate using a lattice coding scheme. It is shown that there is a constant gap between our achievable rate and the information theoretic cut-set bound. This is similar to the recent result by Avestimehr, Diggavi, and Tse who showed such an approximate characterization of the capacity of general Gaussian relay networks. However, our achievability uses a structured code instead of a random one. Using the same idea used in the Gaussian case, we also consider linear finite-field symmetric networks with OC, and characterize the capacity using a linear coding scheme. In the second part, the Gaussian two-way relay channel, where two source nodes exchange messages with each other through a relay, is considered. We assume that all nodes operate in full-duplex mode, and there is no direct channel between the source nodes. We propose an achievable scheme, which is composed of nested lattice codes for the uplink and structured binning for the downlink. The lattice coding scheme for the uplink is essentially the same as that used in the first part of this work, and provides the gain of computation coding. It is also closely related to the concept of network coding for wireless networks. We show that the scheme achieves to within ½ bit the the cut-set bound for all channel parameters, and asymptotically optimal as the signal to noise ratios (SNR) increase. The constant gaps to the capacities obtained in this work do not depend on the other parameters such as SNRs. Therefore, the result is meaningful in high SNR regim...