Physical layer network coding for wireless multi-way relaying with finite signal sets

In this survey article, we consider the wireless multi-way relaying scenario, in which there is no direct link connecting the nodes and multiple nodes exchange information with the help of a relay node. In a multi-way relaying scenario, if several nodes transmit simultaneously, due to the superposition nature of the wireless channel, multiple access interference results at the relay node, which can potentially degrade the performance. However, recent results on physical layer network coding for the two-way relay channel with finite signal sets have shown that the multiple access interference can be effectively tackled by a proper choice of transmission schemes at the nodes. The effect of the multiple access interference is the presence of signal set dependent deep channel fade conditions. For the two-way relay channel, the harmful effect of the deep channel fade conditions have been shown to be avoidable using two techniques: (i) adaptively changing the network coding maps used at the relay node, a process called denoising, which eliminates the harmful effect of the additive noise when a deep channel fade condition occurs (ii) eliminating the occurrence of the deep channel fade conditions at the transmitting nodes itself without any CSIT by Distributed Space Time Coding. We survey the results based on these two schemes for the two-way and three way relaying scenarios and point out some problems which remain unsolved. Towards the end, we discuss about the extension of the schemes developed for the two-way relaying scenario to the multi-way relaying scenario.