Non-orthogonal multiple access (NOMA) has been studied as a promising multiple access technology for optical communication systems due to its superior spectral efficiency. However, the multi-user communication systems that employ NOMA with successive interference cancellation (SIC) suffer from error propagation (EP). Besides, the issue of non-ideal rise and fall time of the received signal can result in severe bit error rate (BER) degradation while decoding by the SIC technique. In this paper, we propose a straightforward two-stage program judgment filter (PJF) for signal reshaping and a SIC-free decoding method for NOMA. Based on the amplitude threshold (AT) decoding method, we demonstrate a real-time, two-user uplink underwater wireless optical communication (UWOC) system via field programmable gate arrays (FPGAs). With a power allocation ratio (PAR) of 2:1 (user 1: user 2), the established real-time NOMA-based UWOC system utilizing commercial light emitting diodes (LEDs) achieves a data rate of 30 Mbps for each user with BERs of 7.8 × 10-6 and 3 × 10-4 for user 1 and user 2, respectively. The results show that the AT-based NOMA can obtain a lower BER compared to the SIC-based NOMA, especially for user 2.