Orthogonal frequency division multiplexing (OFDM) based non-orthogonal multiple access (NOMA) has increased complexity and reduced spectral efficiency in visible light communications (VLC) NOMA compared to radio-frequency NOMA due to non-negative real value constraint on transmit symbols. To address this issue, we propose a generalized non-OFDM based scheme for two scenarios of indoor VLC; i) Multiple access channel (MAC), ii) Broadcast channel (BC). We evaluate the performance of the proposed scheme for MAC using successive interference cancellation (SIC) based decoding, joint maximum likelihood (JML) decoding, and a combination of SIC and JML decoding. For BC, we evaluate the performance using SIC based decoding. It is observed that, for MAC, the proposed scheme with JML decoding performs better than the state-of-the-art orthogonal multiple access both in terms of bit error rate (BER) and computations. For BC, the proposed scheme is computationally efficient with trade-off on BER. © 2012 IEEE.