Analog Network Coding Mappings in Gaussian Multiple-Access Relay Channels

We consider the multiple-access relay channel with two source nodes, one relay node and one destination node. For practical simplicity, we consider orthogonal transmission of the source messages and half-duplex relaying. We also assume that the relay is memoryless and is implemented based on a two-to-one deterministic mapping. Our focus is on proposing and investigating such mappings. Essentially, the proposed relaying functions combine the two incoming analog signals and forward them to the destination, thus we term them as analog network coding mappings. Both linear and non-linear relaying are investigated for the multiple-access relay channel and the special case of the multiple-access two-hop channel. In particular, we suggest to use mappings based on the Archimedean spiral for analog non-linear combining. In addition, we propose to couple spiral mappings with sawtooth-like mappings to exploit the potential side information provided by the direct links of the multiple-access relay channel. In the case of symmetric topology, our proposed scheme can be seen as an extension to the amplify-and-forward scheme, where the asymmetric input/output dimensionality in the relay node is handled before amplifying. We investigate the resulting achievable rate regions and sum rates, and demonstrate significant gains over conventional relaying schemes.