We consider an intelligent reflecting surface (IRS)-aided mobile edge computing (MEC) system, where an IRS is deployed to assist computation offloading from two users to an access point connected with an edge cloud. For the IRS-aided data transmission, in contrast to the conventional non-orthogonal multiple-access (NOMA) and time-division multiple-access (TDMA), we propose a new flexible time-sharing NOMA scheme that allows users to flexibly divide their data into two parts transmitted via NOMA and TDMA, respectively, thus encapsulating both conventional NOMA and TDMA as special cases. We formulate an optimization problem to minimize the sum delay of the two users by designing the IRS passive reflection and users' computation-offloading scheduling under the IRS discrete-phase constraint. Although this problem is non-convex, we obtain its optimal solution for both the cases of infinite and finite cloud computing capacities. Furthermore, we show that NOMA and TDMA based transmissions are preferred in different scenarios, depending on the users' cloud-computing time as well as the rate discrepancy between NOMA and TDMA with IRS.
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