Bounding the Achievable Region of Sparse NOMA

Non-orthogonal multiple access (NOMA) is a promising technology in the design of efficient state-of-the-art communication, particularly 5G and beyond cellular systems. Understanding its fundamental information-theoretic limits is hence of paramount interest. This paper focuses on regular sparse NOMA (where only a fixed and finite number of orthogonal resources is allocated to any designated user, and vice versa), and extends a previous analysis by the authors to a setting where the system comprises two classes of users with different power constraints. Explicit rigorous closed-form analytical inner and outer bounds on the achievable rate (total class throughput) region in the large-system limit are derived. The inner bound is based on the conditional vector entropy power inequality (EPI), while the outer bound relies on a recent strengthened version of the EPI by Courtade. The closed-form bounds provide valuable insights into the potential performance gains of regular sparse NOMA in practically oriented settings, comprising, e.g., a combination of low-complexity devices and broadband users with higher transmit power capabilities, or combinations of cell-edge users with users located close to the cell center. Conditions are identified where superior performance over dense code-domain NOMA is guaranteed, and a relatively small gap to the ultimate performance limits is attainable. The bounds may also serve as a useful tool for future analyses involving interference networks, as, e.g., Wyner-type cellular models.