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This paper investigates the joint design of fronthaul compression and precoding for the downlink of cloud radio access networks (C-RANs). In a C-RAN, a central unit (CU) controls a cluster of radio units (RUs) through low-latency fronthaul links. Most previous works on the design of fronthaul compression and precoding assume constant channels and instantaneous channel state information (CSI) at the CU. This paper, in contrast, concentrates on a more practical scenario with block-ergodic channels and considers either instantaneous or stochastic CSI at the CU. Moreover, the analysis encompasses two types of CU-RU functional splits at the physical layer, which we refer to as compression-after-precoding (CAP) and compression-before-precoding (CBP). With the CAP approach, which is the standard C-RAN solution, all baseband processing is done at the CU. With the CBP scheme, channel encoding and …