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Data transmissions based on Pulse Position Modulation (PPM) and its variants are considered for indoor localization using Visible Light Communication (VLC). To support different illumination levels for pleasant environments and for energy savings when background light is sufficient, light dimming is required. While there are existing PPM based modulation schemes with dimming support, those relying on adjusting the Direct Current (DC) bias or the pulse width suffer from low Signal-to-Noise Ratios (SNRs) at low illumination levels. Other schemes require signalling overheads or high computational complexities in encoding and decoding. These schemes are not suitable for short data transmissions in indoor localization systems with low-complexity mobile receivers. This work proposes a PPM based modulation scheme that supports dimming without signalling overhead and high-complexity encoding/decoding for dimming adjustment. The proposed scheme uses time division between PPM and Inverse PPM (IPPM), with dimming adjusted through varying the time fraction between PPM and IPPM. For each PPM/IPPM data symbol, pulse positions can be mapped to a point in a signal constellation, with one constellation for one dimming level. To provide for flexible dimming in which a transmitter need not inform a receiver which constellation is used (i.e., no signalling overhead), detection of data bits based on multiple signal constellations is investigated. In particular, each data symbol is mapped to a cluster of signal points instead of a single point. The conventional minimum-distance detection is still optimal, though the corresponding bit error rate (BER) depends on the minimum distance between signal clusters instead of between signal points. Finally, for BER improvements, detection based on successive data symbols is investigated.