Geometrically Shaped Constellation in Short-Packet Visible Light Communications for IIoT Applications

Due to the high data rates, license-free operations and inherent security, visible light communication (VLC) is highly valued in Industrial Internet of Things (IIoT) applications. Short packet communication, which offers ultralow latency and efficient resource utilization, is suitable for the low-latency and massive connectivity demand of the IIoT system. It adopts finite blocklength codewords for data transmissions. In this article, we present a general framework of designing geometrically shaped constellations in short-packet VLC with peak and average intensity constraints for IIoT applications. By leveraging tools from large deviation theory, we first characterize the second-order asymptotics of the optimal constellation shaping region under aforementioned intensity constraints, which serves as a good performance metric for the best geometric shaping in finite blocklength. To further incorporate a sufficiently large coding gain and a nearly maximum shaping gain, we construct multidimensional constellations by the nested structure of Construction B lattices, where the constellation shaping is implemented by controlling the boundary of the embedded sublattice, i.e., a strategy called coarsely shaping and finely coding. Fast algorithms for constellation mapping and demodulation are presented as well. As an illustrative example, we present an energy-efficient 24-D constellation design based on the Leech lattice, whose superiority over existing constellation designs is verified by numerical results.