  The three-user finite field multi-way relay channel with correlated sources
is considered. The three users generate possibly correlated messages, and each
user is to transmit its message to the two other users reliably in the Shannon
sense. As there is no direct link among the users, communication is carried out
via a relay, and the link from the users to the relay and those from the relay
to the users are finite field adder channels with additive noise of arbitrary
distribution. The problem is to determine the set of all possible achievable
rates, defined as channel uses per source symbol for reliable communication.
For two classes of source/channel combinations, the solution is obtained using
Slepian-Wolf source coding combined with functional-decode-forward channel
coding.
