# The BER Performance of the LDPC-Coded MPPM over Turbulence UWOC Channels

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## Abstract

**:**

## 1. Introduction

## 2. System and Channel Models

_{0}, and the variance of ${\sigma}_{n}^{2}={N}_{0}/2$. The channel gain is h, which can be expressed as $h={h}_{l}{h}_{f}$, where ${h}_{l}$ is the path loss and is assumed to be unity, ${h}_{f}$ represents the slow-fading coefficient. Here, we use GG distribution to model received optical intensity fluctuation.

## 3. LLR Calculation

## 4. BER Performance without the FEC

## 5. Results and Discussion

^{−5}at the SNRs of 14.4 dB and 19.9 dB, respectively, at moderate (${\sigma}_{I}^{2}=0.5782$) and strong (${\sigma}_{I}^{2}=2.0399$) turbulence. In the absence of the LDPC code, the BERs are higher than 10

^{−2}at the SNR of 22 dB, demonstrating significant coding gain. In weak turbulence with ${\sigma}_{I}^{2}=0.2073$, a code gain of ~12.1 dB is obtained at the BER of 10

^{−4}.

^{−4}, respectively.

^{−4}, respectively. Though the BER performance improves and coding gains get higher for (6, 3), (5, 2) and (4, 1) MPPM, the spectral efficiencies given by $\eta ={\displaystyle \lfloor}{\mathrm{log}}_{2}\left(\begin{array}{c}M\\ w\end{array}\right){\displaystyle \rfloor}/M$ decrease accordingly. This is expected, as MPPM always has a tradeoff between spectral efficiency and power efficiency [27].

## 6. Conclusions

^{−4}for (6, 3), (5, 2) and (4, 1) MPPM scheme in the GG fading channel with a scintillation index of ${\sigma}_{I}^{2}$ = 0.2073. Furthermore, LDPC code with simplified LLRs is suitable for practical implementation because of less computational complexity and no requirement for CSI.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Bit error rate and symbol error rate of the (5, 2) MPPM UWOC system in the absence of fading.

**Figure 4.**BERs of the (5, 2) MPPM UWOC system with/without LDPC code in the GG-distributed fading channel with different scintillation indexes.

**Figure 5.**BERs of the (6, 3) MPPM UWOC system with/without LDPC code in the same weak turbulence channel modeled by different statistical distributions.

**Figure 6.**BERs of the UWOC systems with different modulation schemes in the GG fading channel with a scintillation index of ${\sigma}_{I}^{2}$ = 0.2073.

${\mathit{x}}_{i}$ | ${\mathit{w}}_{i}$ |
---|---|

0.13779347054049237 | 0.308441 |

0.7294545495031706 | 0.40112 |

1.8083429017403165 | 0.218068 |

3.4014336978549595 | 0.0620875 |

5.552496140063418 | 0.00950152 |

8.330152746764144 | 0.000753008 |

11.843785837899944 | 0.0000282592 |

16.279257831377613 | 4.24931 × 10^{−}^{7} |

21.99658581198083 | 1.83956 × 10^{−9} |

29.92069701227372 | 9.91183 × 10^{−}^{13} |

**Table 2.**The parameters of GG-distributed fading channels, adopted from [7].

Channel Condition | a | d | p | ${\mathit{\sigma}}_{\mathit{I}}^{2}$ |
---|---|---|---|---|

Salinity random variations | 7.882 × 10^{−}^{6} | 15.32 | 0.3288 | 0.2073 |

Temperature random variations mixed presence of air bubbles | 0.64 | 1.6668 | 1.038 | 0.5782 |

Random presence of air bubbles | 1.407 × 10^{−}^{7} | 3.764 | 0.1942 | 2.0399 |

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**MDPI and ACS Style**

Jiang, H.; He, N.; Liao, X.; Popoola, W.; Rajbhandari, S.
The BER Performance of the LDPC-Coded MPPM over Turbulence UWOC Channels. *Photonics* **2022**, *9*, 349.
https://doi.org/10.3390/photonics9050349

**AMA Style**

Jiang H, He N, Liao X, Popoola W, Rajbhandari S.
The BER Performance of the LDPC-Coded MPPM over Turbulence UWOC Channels. *Photonics*. 2022; 9(5):349.
https://doi.org/10.3390/photonics9050349

**Chicago/Turabian Style**

Jiang, Hongyan, Ning He, Xin Liao, Wasiu Popoola, and Sujan Rajbhandari.
2022. "The BER Performance of the LDPC-Coded MPPM over Turbulence UWOC Channels" *Photonics* 9, no. 5: 349.
https://doi.org/10.3390/photonics9050349