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Intelligent reflecting surfaces (IRSs) are anticipated to provide reconfigurable propagation environment for next generation communication systems. In this paper, we investigate a downlink IRS-aided multi-carrier (MC) non-orthogonal multiple access (NOMA) system, where the IRS is deployed to especially assist the blocked users to establish communication with the base station (BS). To maximize the system sum rate under network quality-of-service (QoS), rate fairness and successive interference cancellation (SIC) constraints, we formulate a problem for joint optimization of IRS elements, sub-channel assignment and power allocation. The formulated problem is mixed non-convex. Therefore, a novel three stage algorithm is proposed for the optimization of IRS elements, sub-channel assignment and power allocation. First, the IRS elements are optimized using the bisection method based iterative algorithm. Then …