Compound relay channel with informed relay and destination

A two-state compound relay channel is considered where the relay and the destination are informed about the channel state while the source is not. Achievable rates and upper bounds are derived for discrete memoryless and Gaussian models, and specialized to a scenario with orthogonal components. It is shown that, apart from some special cases, optimality conditions valid for decode-and-forward (DF)-based solutions on a standard relay channel do not carry over to a compound setting, and more flexible transmission strategies are generally advantageous. For instance, partial decode-and-forward (PDF) that superimposes transmission of three layers and uses joint decoding at the destination performs better than the standard two-layer PDF with successive decoding, even when the latter is optimal for the regular relay channel. Moreover, the capacity is derived in the special case in which the relay is not active in one state. Extension to the broadcast coding approach, as an alternative to the compound model, is also discussed.