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This letter proposes an inverse source coding scheme to mitigate the severe performance degradation caused by light dimming in visible light communications using on-off keying on reliable links. The proposed scheme meets the ratio of 0's to 1's for the dimming target, and transmission efficiency approaches the theoretical maximum, entropy. It outperforms the existing time-multiplexing scheme, and the difference in performance becomes larger the more the dimming target deviates from 50%. There might be several ways to implement inverse source coding and this letter presents an example utilizing Huffman coding.