Relay networks with orthogonal components

In this paper, we consider a class of relay networks with orthogonal components. We assume transmitted signals at a node to its neighbor nodes are orthogonal, e.g., using frequency division multiplexing (FDM). We first consider a simple discrete memoryless network where there is a source, a destination, and two parallel relays between them. We characterize its capacity under a certain restriction on encoders. For general discrete memoryless relay networks with orthogonal components, we find the capacity if the channels are linear finite field channels with random erasures. For general Gaussian relay networks with orthogonal components, we show an achievable rate based on a sequence of nested lattice codes. The cut-set upper bound and our achievability are within a constant number of bits that depends only on the network topology but not on the channel gains. 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.