Fluid antenna multiple access (FAMA) is a concept capable of massive connectivity on the same physical channel without the need of precoding or interference cancellation, by exploiting a super-high dimensional received signal in the spatial domain from fluid antenna system (FAS). This letter investigates the use of 5G New Radio (NR) Modulation Coding Scheme (MCS) for FAMA systems to improve its connectivity over block fading channels. In particular, we propose an iterative decoding receiver with iterative interference covariance estimation for the coded FAMA system. Extrinsic information transfer (EXIT) chart is used to analyze the performance of the proposed iterative receiver. Both EXIT chart analysis and numerical results show that the proposed receiver outperforms the one that uses fixed covariance in the block fading channel. Also, the results indicate that coded FAMA can serve 100 user terminals (UTs) at the rate of 0.5 bit/s/Hz under rich scattering.