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Intelligent reflecting surface (IRS) as a promising technology rendering high throughput in future communication systems is compatible with various communication techniques such as non-orthogonal multiple-access (NOMA). In this paper, the downlink transmission of IRS-assisted NOMA communication is considered while undergoing imperfect channel state information (CSI). Consequently, a robust IRS-aided NOMA design is proposed by solving the sum-rate maximization problem to jointly find the optimal beamforming vectors for the access point and the passive reflection matrix for the IRS, using the penalty dual decomposition (PDD) scheme. This problem can be solved through an iterative algorithm, with closed-form solutions in each step, and it is shown to have very close performance to its upper bound obtained from perfect CSI scenario. We also present a trellis-based method for optimal discrete phase shift selection of IRS which is shown to outperform the conventional quantization method. Our results show that the proposed algorithms, for both continuous and discrete IRS, have very low computational complexity compared to other schemes in the literature. Furthermore, we conduct a performance comparison from achievable sum-rate standpoint between IRS-aided NOMA and IRS-aided orthogonal multiple access (OMA), which demonstrates superiority of NOMA compared to OMA in case of a tolerated channel uncertainty.