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. Focusing on maximizing the allowed sum-rate, we develop a lattice based coding scheme that generalizes both compute-and-forward and successive Wyner-Ziv coding for this model. The scheme builds on Cover and El Gamal partial-decode-compress-and-forward and is shown to strictly outperform the best of the aforementioned two popular schemes. The results are illustrated through some numerical examples.