  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.
