  In this paper, we propose a novel high dimensional constellation design
scheme for visible light communication (VLC) systems employing red/green/blue
light emitting diodes (RGB LEDs). It is in fact a generalized color shift
keying (CSK) scheme which does not suffer efficiency loss due to a constrained
sum intensity for all constellation symbols. Crucial lighting requirements are
included as optimization constraints. To control non-linear distortion, the
optical peak-to-average-power ratio (PAPR) of LEDs is individually constrained.
Fixing the average optical power, our scheme is able to achieve much lower
bit-error rate (BER) than conventional schems especially when illumination
color is more "unbalanced". When cross-talks exist among the multiple optical
channels, we apply a singular value decomposition (SVD)-based pre-equalizer and
redesign the constellations, and such scheme is shown to outperform
post-equalized schemes based on zero-forcing or linear
minimum-mean-squared-error (LMMSE) principles. To further reduce system BER, a
binary switching algorithm (BSA) is employed the first time for labeling high
dimensional constellation. We thus obtains the optimal bits-to-symbols mapping.
