Energy-Efficient Multidimensional Constellation Based on Leech Lattice for Visible Light Communications

In this paper, a 24-dimensional geometrically-shaped constellation design based on Leech lattice is presented for indoor visible light communications (VLCs) with a peak-and an average-intensity input constraints. Firstly, by leveraging tools from large deviation theory, we characterize second-order asymptotics of the optimal constellation shaping region under aforementioned intensity constraints, which further refine our previous results in [Chen. et. al, 2020]. Within the optimal geometrical shaping region, we develop an energy-efficient 24-dimensional constellation design, where a significant coding gain brought by the Leech lattice and the nearly-maximum shaping gain are incorporated by using a strategy called coarsely shaping and finely coding. Fast algorithms for constellation mapping and demodulation are presented as well. Numerical results verifies the superiority of our results as compared with existing methods.