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.

In this paper, we investigate the capacity of a multiple-input multiple-output (MIMO) optical intensity channel (OIC) with peak- and average-intensity constraints individually imposed on each transmitter. We first consider the case where the average input intensities are required to be equal to preassigned constants due to the requirement of illumination quality and color temperature. For the MIMO OIC with a strongly connected channel graph, we prove that its strongest eigen-subchannel must have positive channel gains, which reveals the underlying relationship between the MIMO OIC and the multiple-input single-output OIC. In the general case, we derive various capacity bounds by standard information theoretic tools and investigate several transceivers with certain architectures. In the special case where the channel rank is one less than the number of transmitters, we derive an equivalent capacity expression from the perspective of convex geometry, and new capacity lower bounds are derived based on this equivalent expression. Finally, the developed results are extended to another type of channels, where the average input intensities are required to be no larger than preassigned constants. These derived bounds are numerically verified to approach the capacity in the low or high signal-to-noise ratio regime.

This paper investigates the capacity of general multiple-input single-output (MISO) optical intensity channels (OICs) under per-antenna peak- and average-intensity constraints. We first consider the MISO equal-cost constrained OIC (EC-OIC), where, apart from the peak-intensity constraint, average intensities of inputs areequal toarbitrarily preassigned constants. The second model of our interest is the MISO bounded-cost constrained OIC (BC-OIC), where, as compared with the EC-OIC, average intensities of inputs areno larger thanarbitrarily preassigned constants. By leveraging tools from quantile functions, stop-loss transform and convex ordering of nonnegative random variables, we prove two decomposition theorems for bounded and nonnegative random variables, based on which we equivalently transform both the EC-OIC and the BC-OIC into respective single-input single-output channels under a peak-intensity and several stop-loss mean constraints. Capacity lower and upper bounds for both channels are established, based on which the asymptotic capacity at high and low signal-to-noise-ratio are determined.

Abstract In this paper, with the assumption of only channel statistics information available at the receivers, a novel concept of multiplicative uniquely decomposable constellations is proposed for multi‐user single‐input multiple‐output (MU‐SIMO) FSO systems in weak atmospheric turbulence, which is modeled by spatially dependent lognormal fading channels. The design enables the fast decoding at the users' sides and meanwhile allows flexibility in assigning each user's ordering to meet different priority needs. Simulation results show that our proposed design has a significant performance improvement over the TDMA scheme at the same rates.

We consider an intensity-modulated (IM) communication system in the presence of Gaussian noise. To improve the reliability of such a system, a space-only constellation-optimal structure was proposed by Zhang under a peak and an average power constraint. However, how to utilize time resource to design signals has been an unsolved problem. In this paper, we design a complexity-efficient coded modem for IM signals under a peak- and an average-power constraint in finite-blocklength regimes. The proposed modem consists of a lattice-based multidimensional constellation bounded by the optimal shaping region, decomposable constellation mapping and demapping based on the fast Fourier transform (FFT), and a fast demodulator with near maximum-likelihood performance. To the authors' best knowledge, for the first time, the FFT and the inverse FFT (IFFT) algorithms are used for constellation mapping to reduce the involved complexity. Both theoretical analysis and Monte Carlo simulation results show that our proposed modem has significant signal-to-noise ratio gains and can support flexible-rate transmission compared to the one-dimensional optimal constellation with Gray labeling.