This work considers a setting in which an encoder wishes to communicate with a decoder through a relay that is connected to the decoder via a finite-capacity link. Motivated by communication on the uplink of a cloud radio access cellular network, it is assumed that the relay compresses and forwards the received signal; moreover, the decoder has side information about the transmitted signal that is subject to fading whose realization is unknown to encoder and relay. A robust transmission and compression strategy is proposed that aims at minimizing the transmitted power under competitive rate optimality constraints. This contrasts with more conventional worst-case or average performance criteria. The transmission strategy is based on a broadcast coding and is parameterized by the maximum tolerable delay in terms of number of fading coherence blocks. Numerical results demonstrate the role of delay and the advantages of broadcast coding over the conventional single-layer transmission.