  Computation off-loading in mobile edge computing (MEC) systems constitutes an
efficient paradigm of supporting resource-intensive applications on mobile
devices. However, the benefit of MEC cannot be fully exploited, when the
communications link used for off-loading computational tasks is hostile.
Fortunately, the propagation-induced impairments may be mitigated by
intelligent reflecting surfaces (IRS), which are capable of enhancing both the
spectral- and energy-efficiency. Specifically, an IRS comprises an IRS
controller and a large number of passive reflecting elements, each of which may
impose a phase shift on the incident signal, thus collaboratively improving the
propagation environment. In this paper, the beneficial role of IRSs is
investigated in MEC systems, where single-antenna devices may opt for
off-loading a fraction of their computational tasks to the edge computing node
via a multi-antenna access point with the aid of an IRS. Pertinent
latency-minimization problems are formulated for both single-device and
multi-device scenarios, subject to practical constraints imposed on both the
edge computing capability and the IRS phase shift design. To solve this
problem, the block coordinate descent (BCD) technique is invoked to decouple
the original problem into two subproblems, and then the computing and
communications settings are alternatively optimized using low-complexity
iterative algorithms. It is demonstrated that our IRS-aided MEC system is
capable of significantly outperforming the conventional MEC system operating
without IRSs. Quantitatively, about $20~\%$ computational latency reduction is
achieved over the conventional MEC system in a single cell of a $300~\rm{m}$
radius and $5$ active devices, relying on a $5$-antenna access point.
