In this paper, we study the benefit of Joint Network Channel Coding (JNCC) and Decoding (JNCD) for half-duplex slow fading Multiple-Access Multiple-Relay Channels (MAMRC), defined as follows: (1) Multiple statistically independent sources communicate with a single destination with the help of multiple relays; (2) Each relay is half-duplex; (3) The links between the different nodes are subject to slow fading and additive white Gaussian noise; (4) Some links interfere. Channel State Information (CSI) is available only at the receivers (relays or destination) and assumed perfect. While the Multiple Access (MA) function is presented generically depending on how the resources are allocated to the sources and relays, the emphasis is on the most spectrally-efficient Non-Orthogonal Multiple-Access (NOMA) where sources and cooperating relays interfere. The relays perform JNCC in combination with Selective Relaying (SR), meaning that they forward a function of the correctly decoded sources' packets to the destination. Practical linear JNCC schemes and the corresponding JNCD architectures are described in detail for NOMA, and shown to perform close to the theoretical limits.