  By exploiting the superiority of non-orthogonal multiple access (NOMA),
NOMA-aided mobile edge computing (MEC) can provide scalable and low-latency
computing services for the Internet of Things. However, given the prevalent
stochasticity of wireless networks and sophisticated signal processing of NOMA,
it is critical but challenging to design an efficient task offloading algorithm
for NOMA-aided MEC, especially under a large number of devices. This paper
presents an online algorithm that jointly optimizes offloading decisions and
resource allocation to maximize the long-term system utility (i.e., a measure
of throughput and fairness). Since the optimization variables are temporary
coupled, we first apply Lyapunov technique to decouple the long-term stochastic
optimization into a series of per-slot deterministic subproblems, which does
not require any prior knowledge of network dynamics. Second, we propose to
transform the non-convex per-slot subproblem of optimizing NOMA power
allocation equivalently to a convex form by introducing a set of auxiliary
variables, whereby the time-complexity is reduced from the exponential
complexity to $\mathcal{O} (M^{3/2})$. The proposed algorithm is proved to be
asymptotically optimal, even under partial knowledge of the device states at
the base station. Simulation results validate the superiority of the proposed
algorithm in terms of system utility, stability improvement, and the overhead
reduction.
