This essay aims to simulate a NOMA downlink system in the power domain and evaluate its performance in terms of information rate. Non-Orthogonal Multiple Access (NOMA) systems have attracted significant interest in the context of next-generation networks for their potential to accommodate a large number of users and theoretically offer superior spectral efficiency compared to traditional Orthogonal Multiple Access (OMA) systems. Our primary goal is to evaluate the simulated system's performance in relation to the Shannon capacity region, which represents the theoretical upper limit of reliable information transmission. Specifically, throughout this work, we demonstrate how closely we can approach the Shannon theoretical limit by implementing M-QAM and turbo codes MODCODs, while maintaining a target frame error rate of $10^{-3}$.