Multidimensional Voronoi constellations (VCs) have been shown to be more power-efficient than quadrature amplitude modulation (QAM) formats given the same uncoded bit error rate, and also have higher achievable information rates. However, a coded modulation scheme that sustains these gains after forward error correction (FEC) coding is still lacking. This paper designs coded modulation schemes with soft-decision FEC codes for VCs, including bit-interleaved coded modulation (BICM) and multilevel coded modulation (MLCM), together with three bit-to-integer mapping algorithms and log-likelihood ratio calculation algorithms. Simulation results show that VCs can achieve up to 1.84 dB signal-to-noise ratio (SNR) gains over QAM with BICM, and up to 0.99 dB SNR gains over QAM with MLCM for the additive white Gaussian noise channel at the bit error rate of$1.81\times 10^{-3}$, with a low decoding complexity.

Voronoi constellations (VCs) are finite sets of vectors of a coding lattice enclosed by the translated Voronoi region of a shaping lattice, which is a sublattice of the coding lattice. In conventional VCs, the shaping lattice is a scaled-up version of the coding lattice. In this paper, we design low-complexity VCs with a cubic coding lattice of up to 32 dimensions, in which pseudo-Gray labeling is applied to minimize the bit error rate. The designed VCs have considerable shaping gains of up to 1.03 dB and finer choices of spectral efficiencies in practice compared with conventional VCs. A mutual information estimation method and a log-likelihood approximation method based on importance sampling for very large constellations are proposed and applied to the designed VCs. With error-control coding, the proposed VCs can have higher information rates than the conventional scaled VCs because of their inherently good pseudo-Gray labeling feature, with a lower decoding complexity.

In a classical 1983 paper, Conway and Sloane presented fast encoding and decoding algorithms for a special case of Voronoi constellations (VCs), for which the shaping lattice is a scaled copy of the coding lattice. Feng generalized their encoding and decoding methods to arbitrary VCs. Less general algorithms were also proposed by Kurkoski and Ferdinand, respectively, for VCs with some constraints on their coding and shaping lattices. In this work, we design VCs with a cubic coding lattice based on Kurkoski's encoding and decoding algorithms. The designed VCs achieve up to 1.03 dB shaping gains with a lower complexity than Conway and Sloane's scaled VCs. To minimize the bit error rate (BER), pseudo-Gray labeling of constellation points is applied. In uncoded systems, the designed VCs reduce the required SNR by up to 1.1 dB at the same BER, compared with the same VCs using Feng's and Ferdinand's algorithms. In coded systems, the designed VCs are able to achieve lower BER than the scaled VCs at the same SNR. In addition, a Gray penalty estimation method for such VCs of very large size is introduced.

Optical signal propagation through underwater channels is affected by three main degrading phenomena, namely, absorption, scattering, and fading. In this paper, we experimentally study the statistical distribution of intensity fluctuations in underwater wireless optical channels with random temperature and salinity variations, as well as the presence of air bubbles. In particular, we define different scenarios to produce random fluctuations on the water refractive index across the propagation path and, then, examine the accuracy of various statistical distributions in terms of their goodness of fit to the experimental data. We also obtain the channel coherence time to address the average period of fading temporal variations. The scenarios under consideration cover a wide range of scintillation index from weak to strong turbulence. Moreover, the effects of beam-expander-and-collimator (BEC) at the transmitter side and aperture averaging lens (AAL) at the receiver side are experimentally investigated. We show that the use of a transmitter BEC and/or a receiver AAL suits single-lobe distributions, such that the generalized Gamma and exponentiated Weibull distributions can excellently match the histograms of the acquired data. Our experimental results further reveal that the channel coherence time is on the order of 10-3s and larger which implies to the slow fading turbulent channels.