  In a multiway relay channel (MWRC), pairwise transmission strategy can be
used to reduce the computational complexity at the relay and the users without
sacrificing the data rate, significantly. The performance of such pairwise
strategies, however, is affected by the way that the users are paired to
transmit. In this paper, we study the effect of pairing on the common rate and
sum rate of an MWRC with functional-decode-forward (FDF) relaying strategy
where users experience asymmetric channel conditions. To this end, we first
develop a graphical model for an MWRC with pairwise transmission strategy.
Using this model, we then find the maximum achievable common rate and sum rate
as well as the user pairings that achieve these rates. This marks the ultimate
performance of FDF relaying in an MWRC setup. Further, we show that the rate
enhancement achieved through the optimal user pairing becomes less pronounced
at higher SNRs. Using computer simulations, the performance of the optimal
pairing is compared with those of other proposed pairings in the literature.
