Turbulence-induced fading is a critical performance degrading factor for underwater wireless optical communication (UWOC) systems. In this paper, we propose a quasi-cyclic (QC) low-density parity-check (LDPC) code with multiple-pulse-position modulation (MPPM) to overcome turbulence-induced fading. MPPM is adopted as a compromise between the low-power efficiency of on–off keying (OOK) and the low bandwidth efficiency of pulse position modulation (PPM). The bit error rate (BER) performance of LDPC-coded MPPM over turbulence UWOC channels is investigated. The log-likelihood ratio (LLR) of MPPM is derived, and a simplified approximation is used for iterative decoding. Subsequently, the closed-form expression of the BER, without forward error correction (FEC) code, is obtained for the generalized-gamma (GG) fading model. Finally, Monte-Carlo (MC) simulation results are provided to demonstrate the correctness of the derived closed-form expressions and the effectiveness of the LDPC code with simplified LLR to improve the BER performance for different MPPM formats over fading channels.

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