# LDPC-Coded CAP with Spatial Diversity for UVLC Systems over Generalized-Gamma Fading Channel
## 1 Introduction  
With increasing oceanic activities, such as environmental monitoring, resource exploration, marine archaeology, and oceanographic-data collection, there has been huge demand for high-speed reliable short-to-medium-range underwater communication [1]. Recently, underwater visible-light communication (UVLC) has drawn significant attention due to the availability of high-bandwidth, high-speed data communication, and low cost [2]. However, the performance of a UVLC system is adversely affected by absorption, scattering, and underwater optical turbulence (UOT). Hence, to realise the full potential of UVLC, appropriate technique(s) should be adopted to alleviate these impairments [3]. Among these impairments, absorption and scattering were extensively studied [4; 5; 6]. UOT results from changes in the refractive index of water caused by random variations of water temperature and salinity, and the presence of air bubbles that result in random fluctuations on the received signal known as turbulence-induced fading. The performance of underwater optical wireless communication systems in the presence of underwater turbulence is often modelled with the log-normal distribution [2; 3; 7; 8]. This is similar to the model used for weak atmospheric turbulence [9]. Recently, there have been various efforts to accurately modeloceanic-turbulence-induced fading [1; 10; 11]. It was shown that generalized-gamma (GG) and exponential Weibull distributions can excellently model fading induced by weak-to-strong UOT [11]. In fact, it was shown that many important statistical distributions to model optical turbulence, such as Weibull, gamma, Nakagami-\(m\), exponential, and Rayleigh, are special cases of GG distribution [12]. To mitigate the effects of turbulence-induced fading, several techniques, such as forward-error correction (FEC) [13], diversity [2; 3; 8], and multihop relaying [7], were suggested. For short-range communication, coding and diversity are preferred due to low complexity and ease of implementation. Low-density parity-check (LDPC) code is a highly efficient linear block code characterised by a sparse parity-check matrix that results in low hardware complexity. The error-correction performance of LDPC can approach the Shannon limit in an additive white Gaussian noise (AWGN) channel [14]. LDPC codes provide higher code gain, and perform significantly better than turbo-products and Reed-Solomon codes [13; 15]. Furthermore, the decoding complexity of LDPC codes increases linearly in comparison to the exponential increment in turbo code. Thus, LDPC has been widely employed in optical communication [13; 16]. Meanwhile, spatial diversity is considered as one of the most effective solutions to mitigate turbulence-induced fading. Spatial diversity also decreases the possibility of temporary blockage due to an obstruction (e.g., fish) [8]. Additionally, the selection of the modulation scheme is equally vital for the optimal performance of UVLC systems. Carrierless amplitude and phase (CAP) modulation is an attractive scheme in UVLC due to simple implementation, low energy consumption, and high spectral efficiency [17]. CAP modulation is more suitable to intensity-modulation and direct-detection (IM/DD)-based optical communication than its counterpart, quadrature-amplitude modulation (QAM), as the CAP is realised using a pair of orthogonal filters to transmit two parallel streams of data without a carrier [18]. In addition, CAP has similar spectral efficiency as that of orthogonal frequency division multiplexing (OFDM) with a lower peak-to-average-power-ratio (PAPR) than that of OFDM [19]. This analysis suggests that combining efficient modulation with effective FEC and diversity offers optimal performance for UVLC systems. Hence, in this study, we propose an LDPC-coded CAP modulation scheme with spatial diversity to improve the performance of UVLC systems over a UOT-induced fading channel.