A multiway relay channel with balanced sources

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 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 P*, we give a balanced-information regularity condition for P*, and we express P* in terms of conditional multiple-mutual information. Finally, we show that P* is useful for a centralized storage problem.