  To mitigate computational power gap between the network core and edges,
mobile edge computing (MEC) is poised to play a fundamental role in future
generations of wireless networks. In this letter, we consider a non-orthogonal
multiple access (NOMA) transmission model to maximize the worst task to be
offloaded among all users to the network edge server. A provably convergent and
efficient algorithm is developed to solve the considered non-convex
optimization problem for maximizing the minimum number of offloaded bits in a
multi-user NOMAMEC system. Compared to the approach of optimized orthogonal
multiple access (OMA), for given MEC delay, power and energy limits, the
NOMA-based system considerably outperforms its OMA-based counterpart in MEC
settings. Numerical results demonstrate that the proposed algorithm for
NOMA-based MEC is particularly useful for delay sensitive applications.
