  The L-user additive white Gaussian noise multiway relay channel is
investigated, where L users exchange information at the same rate through a
single relay. A new achievable rate region, based on the
functional-decode-forward coding strategy, is derived. For the case where there
are three or more users, and all nodes transmit at the same power, the capacity
is obtained. For the case where the relay power scales with the number of
users, it is shown that both compress-forward and functional-decode-forward
achieve rates within a constant number of bits of the capacity at all SNR
levels; in addition, functional-decode-forward outperforms compress-forward and
complete-decode-forward at high SNR levels.
