Cloud radio access networks (C-RAN) gained much attention thanks to their abilities in mitigating interference and providing high data rates by coordinating multiple Remote Radio Heads (RRHs). This paper considers the use of rate aware instantly decodable network coding (RA-IDNC) as a mean to accelerate the broadcast of a set of messages to a set of users in a C-RAN setting. While previous works focus either on rate-unaware IDNC or rate adaptation for traditional single transmitter systems, this paper extends the results to C-RANs. The various ergodic capacities of the different users to the different RRHs bring a new trade-off between the number of scheduled users and the transmission rates. The proposed framework incorporates such information in the network coding decisions, so as the scheduled users, coded messages, and transmission rates reduce the overall completion time. Given the intractability of the problem, the paper proposes relaxing the optimization by an online approach involving an anticipated version of the completion time which allows mapping the possible associations between users, RRHs, coded packets, and transmission rates to vertices in a newly designed graph. Afterward, the online completion time reduction problem is shown to be equivalent to a maximum weight independent set problem over the proposed graph. Simulation results reveal that the proposed scheme achieves substantial performance gain over uncoded and NC rate-unaware algorithms.