  This paper investigates an uplink non-orthogonal multiple access (NOMA)-based
mobile-edge computing (MEC) network. Our objective is to minimize a linear
combination of the completion time of all users' tasks and the total energy
consumption of all users including transmission energy and local computation
energy subject to computation latency, uploading data rate, time sharing and
edge cloud capacity constraints. This work can significantly improve the energy
efficiency and end-to-end delay of the applications in future wireless
networks. For the general minimization problem, it is first transformed into an
equivalent form. Then, an iterative algorithm is accordingly proposed, where
closed-form solution is obtained in each step. For the special case with only
minimizing the completion time, we propose a bisection-based algorithm to
obtain the optimal solution. Also for the special case with infinite cloud
capacity, we show that the original minimization problem can be transformed
into an equivalent convex one. Numerical results show the superiority of the
proposed algorithms compared with conventional algorithms in terms of
completion time and energy consumption.
