# The BER Performance of the LDPC-Coded MPPM over Turbulence UWOC Channels
## 1 Introduction
System size and cost increase as aperture area increases, while performance gain saturates due to background noise. The channel coding technique can substantially reduce the error rate in weak turbulence channels. However, it should be combined with other techniques to combat the degrading effects in moderate to strong turbulence [22]. UWOC performance also greatly depends on the modulation scheme. Modulation schemes are based on spectral efficiency, power efficiency and implementation complexity. Due to implementation simplicity, UWOC usually employs intensity modulation with direct detection (IM/DD), rather than a coherent technique. Subcarrier intensity modulation (SIM), such as phase-shift keying (PSK) and quadrature amplitude modulation (QAM), can effectively exploit bandwidth and improve error performance, but has issues, such as clipping requirements, limited modulation index, and susceptibility to nonlinearity [23]. Furthermore, to overcome adverse effects of strong turbulence on the performance of QAM/PSK, adaptive modulation and diversity/coding are required [24; 25; 26]. On-off keying (OOK) and pulse position modulation (PPM) schemes are widely used in optical communication because of their simplicity. OOK format has superior bandwidth efficiency, but inferior average power efficiency compared with PPM. Additionally, the OOK scheme requires an adaptive threshold to achieve optimal detection in turbulent channels. To overcome these drawbacks, power-efficient multipulse PPM (MPPM) can be adopted as a tradeoff between OOK and PPM. The MPPM scheme has higher power efficiency compared to OOK and higher bandwidth efficiency compared to the PPM [27]. Optical sources can be efficiently driven with a large current for pulse modulation, ensuring a relatively high signal-to-noise ratio (SNR) [28]. Several works reported the performance of the MPPM-based free-space optical (FSO) and UWOC systems over turbulent channels. The study in [29] presented the performance of PPM and MPPM formats in conjunction with a binary convolutional code and iterative soft-decision detection for the FSO communication with weak turbulence modeled by a log-normal distribution. The influence of bit-symbol mapping of MPPM on the iterative receiver performance was analyzed and then provided a design rule to obtain optimal mappings for the iterative detection scheme. The symbol error rate (SER) performance of MPPM-basedFSO system with fixed decision threshold (FDT), optimized decision threshold (ODT) and dynamic decision threshold (DDT) over EW-distributed fading channels were studied in [30]. The study derived closed-form SER expressions for the three thresholds scheme and investigated the effects of aperture averaging. It was shown that the performance of DDT is better than those of FDT and ODT. However, the DDT scheme is computationally complex due to requirements for channel state information (CSI). Furthermore, combining effects of EW-distributed fading and pointing errors, SER performance of (\(m\), \(n\)) MPPM-based FSO system with a new soft decoder is studied in [31]. The decoder considers the largest \(m\) slots of a received signal block (\(n\) slots) as the signal slots without CSI. The new soft-decision technique outperforms the DDT scheme. In [32], comprehensive theoretical SER expressions (not closed-form) for soft-decision MPPM, without CSI, and simplified expressions for fast and slow fading for the FSO non-memoryless channels were derived. The numerical and simulation results for log-normal and gamma-gamma fading were presented. Taking into account the effects of inter-symbol interference, oceanic turbulence and receiver noise, the BER performance of spatial diversity with MPPM receivers applied to UWOC systems operating over log-normal turbulence was investigated in [33]. For the UWOC systems affected by salinity turbulence, the BER of variable weight MPPM coding schemes was evaluated, based on Weibull distribution in [34].