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In this article, we design an end-to-end free-space optical (FSO) communication coding scheme for deep space exploration. Take the Mars exploration as an example, we first establish the synodic period FSO channel model by taking into account the solar scintillation, and derive the corresponding upper bound of bit error rate (BER) for $L$-ary pulse position modulation (LPPM). Then, we propose a staircase code-ordered statistics decoder (SC-OSD) algorithm for staircase low density parity check (LDPC) codes under synodic period FSO channel, and derive the probability density function (PDF) and Gaussian approximation of the ordered statistics of the SC-OSD algorithm, which provide a guideline to derive a lower bound of block error rate (BLER) and reduce the decoding complexity of SC-OSD. Furthermore, we propose a soft OSD-sliding window decoding (SOSD-SWD) algorithm for staircase LDPC codes under scintillation states to address the error floor problem in conventional SWD decoder. Simulation results validate that the proposed SOSD-SWD algorithm can achieve much lower BER than the related algorithms in all scintillation conditions, and shed light to tradeoff the achievable BER and complexities under different scintillation conditions.

Synodic Period Channel Modeling and Coding Scheme for Deep Space Optical Communications