Opportunistic pair-wise compute-and-forward in multi-way relay channels

In this paper, we propose a novel opportunistic pair-wise transmission scheme in a multi-way relay channel (MWRC), in which multiple users exchange information via a common relay. We investigate pair-wise compute-and-forward for MWRCs by exploiting the multi-user fading channels. Conventionally, a pair-wise physical-layer network coding scheme with binary phase shift keying modulation was studied for a MWRC. In this paper, the proposed opportunistic pair-wise compute-and-forward employs high level modulation with nested lattice codes to improve the sum-rate of multi-user transmission. We demonstrate that this novel opportunistic pair-wise transmission has a 2 bits/s/Hz improvement in the sum-rate performance at signal-to-noise ratio of 30 dB for a 4-user MWRC. For the same MWRC, up to 4.5 dB gain or 2.5 dB gain can be achieved for an uncoded or a channel-coded system, respectively, at the frame error probability of 10-2.