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This paper develops a binary decomposition for the peak-constrained intensity-modulation with direct-detection (IM/DD) channel. Then, it uses this decomposition, which we call a Vector Binary Channel (VBC), to propose simple binary coding schemes. The VBC consists of bit-pipes and, different from the Avestimehr-Diggavi-Tse linear deterministic model, captures interactions between bit-pipes thus preserves capacity. Two practical coding schemes are then designed for the VBC. The first is an Independent Coding scheme which encodes independently and decodes successively while ignoring the dependence between noises on different bit-pipes. The second improves upon the first by exploiting the knowledge of noises on previously decoded bit-pipes as a state for the current decoding operation. The achievable rates of the schemes are compared numerically with capacity, and shown to perform well with …