Performance bounds for coded free-space optical communications through atmospheric turbulence channels

Error-control codes can help to mitigate atmospheric turbulence-induced signal fading in free-space optical communication links using intensity modulation/direct detection (IM/DD). Error performance bound analysis can yield simple analytical upper bounds or approximations to the bit-error probability. We first derive an upper bound on the pairwise codeword-error probability for transmission through channels with correlated turbulence-induced fading, which involves complicated multidimensional integration. To simplify the computations, we derive an approximate upper bound under the assumption of weak turbulence. The accuracy of this approximation under weak turbulence is verified by numerical simulation. Its invalidity when applied to strong turbulence is also shown. This simple approximate upper bound to the pairwise codeword-error probability is then applied to derive an upper bound to the bit-error probability for block codes, convolutional codes, and turbo codes for free-space optical communication through weak atmospheric turbulence channels. We also discuss the choice of interleaver length in block codes and turbo codes based on numerical evaluation of our performance bounds.