Wireless network-coded four-way relaying using Latin Hyper-Cubes

This paper deals with physical layer network-coding for the four-way wireless relaying scenario where four nodes A, B, C and D wish to communicate their messages to all the other nodes with the help of the relay node R. The scheme given in the paper is based on the denoise-and-forward scheme proposed first by Popovski et al. in [1]. Intending to minimize the number of channel uses, the protocol employs two phases: Multiple Access (MA) phase and Broadcast (BC) phase with each phase utilizing one channel use. This paper does the equivalent for the four-way relaying scenario as was done for the two-way relaying scenario by Koike-Akino et al. [2], and for three-way relaying scenario in [3]. It is observed that adaptively changing the network coding map used at the relay according to the channel conditions greatly reduces the impact of multiple access interference which occurs at the relay during the MA phase. These network coding maps are so chosen so that they satisfy a requirement called exclusive law. We show that when the four users transmit points from the same M-PSK constellation, every such network coding map that satisfies the exclusive law can be represented by a 4-fold Latin Hyper-Cube of side M. The network code map used by the relay for the BC phase is explicitly obtained and is aimed at reducing the effect of interference at the MA stage.