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We have proposed a variable-rate multi-pulse pulse position modulation, for visible light communication system based on white LEDs, to achieve joint brightness control and data transmission. Conventionally either pulse width modulation or pulse amplitude modulation is used for brightness control and some variants of pulse position modulation are employed for data transmission. The need for using two different modulation schemes to meet the objectives make the system design complex. Our proposed approach eliminates the use of either pulse width modulation or pulse amplitude modulation and still achieves brightness control. For the proposed modulation, achievable resolution of the brightness control depends on the number of slots used for one information symbol transfer and the resulting code-rate for data transmission depends on the number of pulsed slots per symbol. Simple iterative algorithms for encoder and decoder implementation are developed. Numerical results for performance evaluation show the effectiveness of our proposed approach. We have also obtained experimental results to analyze the effect of brightness-index on symbol error rate.