This paper introduces new approaches for combining non-orthogonal multiple access with distributed antenna systems. The study targets a minimization of the total transmit power in each cell, under user rate and power multiplexing constraints. Several new suboptimal power allocation techniques are proposed. They are shown to yield very close performance to an optimal power allocation scheme. Also, a new approach based on mutual successive interference cancellation of paired users is proposed. Different techniques are designed for the joint allocation of subcarriers, antennas, and power, with a particular care given to maintain a moderate complexity. The coupling of non-orthogonal multiple access to distributed antenna systems is shown to greatly outperform any other combination of orthogonal/non-orthogonal multiple access schemes with distributed or centralized deployment scenarios.