A fog-radio access network (F-RAN) architecture is studied for an Internet-of-Things (IoT) system in which wireless sensors monitor a number of multi-valued events and transmit in the uplink using grant-free random access to multiple edge nodes (ENs). Each EN is connected to a central processor (CP) via a finite-capacity fronthaul link. In contrast to conventional information-agnostic protocols based on separate source-channel (SSC) coding, where each device uses a separate codebook, this paper considers an information-centric approach based on joint source-channel (JSC) coding via a non-orthogonal generalization of type-based multiple access (TBMA). By leveraging the semantics of the observed signals, all sensors measuring the same event share the same codebook (with non-orthogonal codewords), and all such sensors making the same local estimate of the event transmit the same codeword. The F-RAN architecture directly detects the events values without first performing individual decoding for each device. Cloud and edge detection schemes based on Bayesian message passing are designed and trade-offs between cloud and edge processing are assessed.