  We consider a joint source-channel coding problem on a finite-field multiway
relay channel, and we give closed-form lower and upper bounds on the optimal
source-channel rate. These bounds are shown to be tight for all discrete
memoryless sources in a certain class $\mathcal{P}^*$, and we demonstrate that
strict source-channel separation is optimal within this class. We show how to
test whether a given source belongs to $\mathcal{P}^*$, we give a
balanced-information regularity condition for $\mathcal{P}^*$, and we express
$\mathcal{P}^*$ in terms of conditional multiple-mutual informations. Finally,
we show that $\mathcal{P}^*$ is useful for a centralised storage problem.
