Cloud radio access network (C-RAN) is a promising technology for fifth-generation (5G) cellular systems. However the burden imposed by the huge amount of data to be collected (in the uplink) from the radio remote heads (RRHs) and processed at the base band unit (BBU) poses serious challenges. In order to reduce the computation effort of minimum mean square error (MMSE) receiver at the BBU the Gaussian message passing (MP) together with a suitable sparsification of the channel matrix can be used. In this paper we propose two sets of solutions, either centralized or distributed ones. In the centralized solutions, we propose different approaches to sparsify the channel matrix, in order to reduce the complexity of MP. However these approaches still require that all signals reaching the RRH are conveyed to the BBU, therefore the communication requirements among the backbone network devices are unaltered. In the decentralized solutions instead we aim at reducing both the complexity of MP at the BBU and the requirements on the RRHs-BBU communication links by pre-processing the signals at the RRH and convey a reduced set of signals to the BBU.