We study the transmission over a cloud radio access network in which multiple base stations (BS) are connected to a central processor (CP) via finite-capacity backhaul links. We propose two lattice-based coding schemes. In the first scheme, the base stations decode linear combinations of the transmitted messages, in the spirit of compute-and-forward (CoF), but differs from it essentially in that the decoded equations are remapped to linear combinations of the channel input symbols, sent compressed in a lossy manner to the central processor, and are not required to be linearly independent. Also, by opposition to the standard CoF, an appropriate multi-user decoder is utilized to recover the sent messages. The second coding scheme generalizes the first one by also allowing, at each relay node, a joint compression of the decoded equation and the received signal. Both schemes apply in general, but are more suited for situations in which there are more users than base stations. We show that both schemes can outperform standard CoF and successive Wyner-Ziv schemes in certain regimes, and illustrate the gains through some numerical examples.