We study random access for machine-type commu- nications (MTC) based on the notion of compressive sensing (CS) over a distributed input distributed output (DIDO) system consisting of a number of remote radio heads (RRHs) that are closely located to devices. In a DIDO system, each active device can have a signature that depends on its connectivity to RRHs and the signatures of active devices are estimated and used for signal detection in random access using a CS algorithm. We derive a relation between key parameters such as the average number of active devices and the number of the outputs of a DIDO system for a good performance.