This paper investigates practical 5G strategies for power-balanced non-orthogonal multiple access (NOMA). By allowing multiple users to share the same time and frequency, NOMA can scale up the number of served users and increase spectral efficiency compared with existing orthogonal multiple access (OMA). Conventional NOMA schemes with successive interference cancellation (SIC) do not work well when users with comparable received powers transmit together. To allow power-balanced NOMA (more exactly, near power-balanced NOMA), this paper investigates a new NOMA architecture, named Network-Coded Multiple Access (NCMA). A distinguishing feature of NCMA is the joint use of physical-layer network coding (PNC) and multiuser decoding (MUD) to boost NOMA throughputs. We first show that a simple NCMA architecture in which all users use the same modulation, referred to as rate-homogeneous NCMA, can achieve substantial throughput improvement over SIC-based NOMA under near power-balanced scenarios. Then, we put forth a new NCMA architecture, referred to as rate-diverse NCMA, in which different users may adopt different modulations commensurate with their relative SNRs. A challenge for rate-diverse NCMA is the design of a channel-coded PNC system. This paper is the first attempt to design channel-coded rate-diverse PNC. Experimental results on our software-defined radio prototype show that the throughput of rate-diverse NCMA can outperform the state-of-the-art rate-homogeneous NCMA by 80%. Overall, rate-diverse NCMA is a practical solution for near power-balanced NOMA.