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.

In this paper, we study two types of optical wireless channels under average-intensity constraints. One is called the Gaussian optical intensity channel, where the channel output models the converted electrical current corrupted by additive white Gaussian noise. The other one is the Poisson optical intensity channel, where the channel output models the number of received photons whose arrival rates are corrupted by a dark current. When the average input intensity ε is small, the capacity of the Gaussian optical intensity channel is shown to scale as ε√log1/ε/2, and the capacity of the Poisson optical intensity channel as ε log log1/ε. This closes the gaps between previously-derived upper and lower bounds on the asymptotic capacity of these two types of channels.

This paper investigates the capacity of an optical wireless channel with an average-intensity constraint in the low signal-to-noise ratio (SNR) regime. When the average intensity of the input is no larger than a small E, the capacity scales as$\mathcal{E} \sqrt{\frac{\log \frac{1}{\varepsilon}}{2}}$

This paper studies the capacity of optical wireless relay channels under peak- or both peak- and average-intensity constraints. Capacity upper bounds are derived by applying the cutset bounding techniques combined with the maximum entropy argument or the capacity duality expression, and ca-pacity lower bounds by using the decode-and-forward coding scheme and decomposition results of certain random variables. The derived bounds are numerically shown to be fairly close in the high signal-to-noise ratio regime.

This paper studies the secrecy capacity of the visible light communication (VLC) wiretap channel under a per-antenna peak-intensity constraint and a per-antenna average-intensity constraint. The focus is on the scenario with one transmitter, one legitimate user, and one eavesdropper, all equipped with multiple antennas. Considering various quantity configurations of the number of transmitting and receiving antennas, we first derive a closed-form secrecy rate exploiting the truncated exponential distribution. Based on this, full-connected and sub-connected precoding architectures are proposed to enhance the confidentiality of this multiple-input multiple-output (MIMO) VLC wiretap channel. Simulation results demonstrate that the proposed precoding schemes significantly improve the secrecy performance of the MIMO-VLC wiretap channel.

This paper investigates the capacity region of the optical intensity broadcast channels (OI-BCs), where the input is subject to a peak-intensity constraint, an average-intensity constraint, or both. By leveraging the decomposition results of several random variables, i.e., uniform, exponential, and truncated exponential random variables, and adopting a superposition coding (SC) scheme, the inner bound on the capacity region is derived. Then, the outer bound is derived by applying the conditional entropy power inequality (EPI). In the high signal-to-noise ratio (SNR) regime, the inner bound asymptotically matches the outer bound, thus characterizing the high-SNR asymptotic capacity region. The bounds are also extended to the general$K$-user BCs without loss of high-SNR asymptotic optimality.

This paper investigates the sum-capacity of two-user optical intensity multiple access channels with a per-user peak- or average-intensity constraint. By leveraging tools on decomposition of random variables, we derive lower bounds on the sum-capacity. In the high signal-to-noise ratio (SNR) regime, they asymptotically match the sum-capacity. In particular, for the peak-intensity constrained channel, our result closes the high-SNR asymptotic sum-capacity gap in the existing works.

This paper investigates the sum-capacity of two-user optical intensity multiple access channels with per-user peak- or/and average-intensity constraints. By leveraging tools from the decomposition of certain distributions, we derive several lower bounds on the sum-capacity. In the high signal-to-noise ratio (SNR) regime, some bounds asymptotically match or approach the sum-capacity, thus closing or reducing the existing gaps to the high-SNR asymptotic sum-capacity. At moderate SNR, some bounds are also fairly close to the sum-capacity.

The diversity-multiplexing tradeoff (DMT) provides a fundamental performance metric for different multiple-input multiple-output (MIMO) schemes in wireless communications. In this paper, we explore the block fading optical wireless communication (OWC) channels and characterize the DMT in the presence of both optical peak- and average-power constraints. Three different fading distributions are considered, which reflect different channel conditions. In each channel condition, we obtain the optimal DMT when the block length is sufficiently large, and we also derive the lower and upper bounds of the DMT curve when the block length is small. These results are dramatically different from the existing DMT results in radio-frequency (RF) channels. These differences may be due to the fact that the optical input signal is real and bounded, while its RF counterpart is usually complex and unbounded.

This paper studies the diversity-multiplexing tradeoff (DMT) for the block fading optical wireless communication (OWC) channel when the number of transmit antennas is not less than that of receive antennas. Inputs in this channel represent optical intensities, and hence are real-valued and non-negative. Moreover, inputs are subject to a per-antenna peak-power and a total average-power constraint. Considering these input constraints and assuming the channel fading follows the negative exponential distribution, we establish the outage diversity and average error probability bounds by using a random truncated exponential coding argument. By these derived bounds, we characterize the optimal DMT curve. Interestingly, the DMT result is fundamentally different from its counterpart in traditional radio frequency (RF) channels. This is due to the fact that inputs in this channel are real-valued and bounded, while in RF channels inputs are usually complex-valued and unbounded.

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.

This paper studies the capacity of a general multiple-input multiple-output (MIMO) free-space optical intensity channel under a per-input-antenna peak-power constraint and a total average-power constraint over all input antennas. The focus is on the scenario with more transmit than receive antennas. In this scenario, different input vectors can yield identical distributions at the output, when they result in the same image vector under multiplication by the channel matrix. We first determine the most energy-efficient input vectors that attain each of these image vectors. Based on this, we derive an equivalent capacity expression in terms of the image vector, and establish new lower and upper bounds on the capacity of this channel. The bounds match when the signal-to-noise ratio (SNR) tends to infinity, establishing the high-SNR asymptotic capacity. We also characterize the low-SNR slope of the capacity of this channel.

This paper investigates the capacity of block fading optical intensity channels with more transmit than receive antennas under different assumptions on the transmitter's channel state information (CSI). Lower and upper bounds on the capacities are derived using the entropy power inequality (EP!) and a dual expression for capacity. Our lower bounds for perfect and partial CSI utilize a transmit-antenna cooperation strategy based on minimum-energy signaling, which we proposed recently. For perfect CSI, this lower bound matches the upper bound asymptotically in the high signal-to-noise ratio (SNR) regime. For imperfect CSI, our lower bound is close to its perfect-CSI counterpart.

The capacity under strong asynchronism was recently shown to be essentially unaffected by the imposed decoding delay-the elapsed time between when information is available at the transmitter and when it is decoded-and the output sampling rate. This paper shows that, in contrast with capacity, the second-order term in the maximum rate expansion is sensitive to both parameters. When the receiver must locate the sent codeword exactly and therefore achieve minimum delay equal to the blocklength n, the second-order term in the maximum rate expansion is of order Θ(1/p) for any sampling rate ρ = O(1/√n) (and ρ = ω(1/n) for otherwise reliable communication is impossible). Instead, if ρ = ω(1/√n), then the second-order term is the same as under full sampling and is given by a standard Θ(√n) term. However, if the delay constraint is only slightly relaxed to n(1+o(1)), then the above order transition (for ρ = O(1/√n) and ρ = w(1/√n)) vanishes and the secondorder term remains the same as under full sampling for any ρ = ω(1/n).

This paper investigates the capacity of the multiple- input multiple-output free-space optical intensity channel under a per-input-antenna peak-power constraint and a total average-power constraint over all input antennas. Our work considers the setup with more transmit than receive antennas, and characterizes capacity as an alternative optimization problem over the distribution of the input vector times the channel matrix. This alternative capacity expression is then used to obtain upper and lower bounds on the capacity, which match asymptotically in the high signal-to-noise ratio regime.

This paper establishes non-asymptotic tradeoffs between detection delay, output sampling rate, and communication rate for bursty communication. These tradeoffs imply regimes where the gap to capacity is captured by the inverse of the sampling rate rather than the usual dispersion.