Next-generation multiple access (NGMA) serves as an umbrella term for transmission schemes distinct from conventional orthogonal methods. A key candidate of NGMA, non-orthogonal multiple access (NOMA), emerges as a solution to enhance connectivity by allowing multiple users to share time, frequency, and space concurrently. However, NOMA faces challenges in implementation, particularly in canceling inter-user interference. In this paper, we discuss the principles behind NOMA and review conventional NOMA methods. Then, to address these challenges, we present asynchronous transmission and interference-aware modulation techniques, enabling decoding without successive interference cancellation. The goal is to design constellations that dynamically adapt to interference, minimizing bit error rates (BERs) and enhancing user throughput in the presence of inter-user, inter-carrier, and inter-cell interference. The traditional link between minimizing BER and increasing spectral efficiency is explored, with deep autoencoders for end-to-end communication emerging as a potential solution to improve BERs. Interference-aware modulation can revolutionize constellation design for non-orthogonal channels. Rate-splitting multiple access (RSMA) is another promising interference management technique in multi-user systems. In addition to addressing challenges in finite-alphabet NOMA, this paper offers new insights and provides an overview of code-domain NOMA, trellis-coded NOMA, and RSMA as key NGMA candidates. We also discuss the evolution of channel coding toward low-latency communication and examine modulation and coding schemes in 5G networks. Finally, we highlight future research directions, emphasizing their importance for realizing NOMA from concept to functional technology.
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