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Optical wireless communication (OWC) has the potential to provide high communication speeds that support the massive use of the Internet that is expected in the near future. In OWC, optical access points (APs) are deployed on the celling to serve multiple users. In this context, efficient multiple access schemes are required to share the resources among the users and align multi-user interference. Recently, non-orthogonal multiple access (NOMA) has been studied to serve multiple users simultaneously using the same resources, while a different power level is allocated to each user. Despite the acceptable performance of NOMA, users might experience a high packet loss due to high noise, which results from the use of successive interference cancelation (SIC). In this work, random linear network coding (RLNC) is proposed to enhance the performance of NOMA in an optical wireless network where users are divided into multicast groups, and each group contains users that slightly differ in their channel gains. Moreover, a fixed power allocation (FPA) strategy is considered among these groups to avoid complexity. The performance of the proposed scheme is evaluated in terms of total packet success probability. The results show that the proposed scheme is more suitable for the network considered compared to other benchmark schemes such as traditional NOMA and orthogonal transmission schemes. Moreover, the total packet success probability is highly affected by the level of power allocated to each group in all the scenarios.