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.

I. Background and Preliminaries

Physical layer network coding for the two-way relay channel exploits the multiple access interference occurring at the relay so that the communication between the end nodes can be done using a two stage protocol. This two-stage protocol was first introduced in [4], and [5], [6] deal with the information theoretic studies for the scheme. In [2], modulation schemes to be used at the nodes for uncoded transmission for the two-way relaying were studied. Work done for the relay channels with three or more user nodes is given in [3], [7], , , [10], either use more than two channel uses, which makes the throughput performance of our scheme better than the other existing schemes, or, deal with the information theoretic aspects of multi-way relaying. Our work in this paper further extends the approach used in [3] to four-way relaying. The scheme we state in this paper, uses totally two channel uses for the information exchange. We consider the four-way wireless relaying scenario shown in Fig. 1, where four-way data transfer takes place among the nodes A, B, C and D with the help of the relay R assuming that the three nodes operate in half-duplex mode. The relaying protocol consists of two phases, multiple access (MA) phase, consisting of one channel use during which A, B, C and D transmit to R; and broadcast (BC) phase, in which R transmits to A, B, C and D in a single channel use. Network Coding is employed at R in such a way that A(/B/C/D) can decode B's, C's and D's(/A's, C's and D's/A',B's and C's) messages, given that A(/B/C/D) knows its own message. Our physical layer network coding strategy uses a mathematical structure called a Latin Hyper-Cube defined as follows: Fig. 1. A four-way relay channel