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The nonlinearity of a light-emitting diode (LED) limits the system performance of a visible light communications (VLC) system. Many nonlinearity mitigation methods have been studied. Recent technology advances in the micro-LED array have provided a simple alternative to deal with the system nonlinearity. In this paper, we study the approach of providing multiple access for the VLC system with the micro-LED array. A code-division multiple-access (CDMA) scheme that enables multiple access with variable data rate is proposed. In addition, the proposed system architecture is immune to the nonlinearity of the micro-LED array, thus providing optimal system performance. Simulations and laboratory experiments show the robustness and consistency of the proposed scheme.