  The linear shift deterministic Y-channel is studied. That is, we have three
users and one relay, where each user wishes to broadcast one message to each
other user via the relay, resulting in a multi-way relaying setup. The cut-set
bounds for this setup are shown to be not sufficient to characterize its
capacity region. New upper bounds are derived, which when combined with the
cut-set bounds provide an outer bound on the capacity region. It is shown that
this outer bound is achievable, and as a result, the capacity region of the
linear shift deterministic Y-channel is characterized.
