Instantaneous relaying for the 3-way relay channel with circular message exchanges

The 3-user discrete memoryless multi-way relay channel with circular message exchange and instantaneous relaying is investigated. We first show that this channel is effectively a 3-user interference channel with receiver message side information for every fixed (and instantaneous) relay mapping. Then, we extend the Han-Kobayashi coding scheme to this channel. Finally, we apply these results to Gaussian channels with amplify-and- forward relaying and present numerical results showing the gain of the proposed scheme compared to the state of the art.