For free-space optical (FSO) links in turbulent atmosphere modeled by gamma-gamma distributions, an approximation of the pairwise error probability (PEP) was derived for on-off keying in a recently published paper. It has been assumed that the channel state is perfectly known to the receiver and that the fading samples are independent and identically distributed. Based on these conditions, we show in this letter that the approximation can be replaced by a closed-form solution, disregarding a finite-limit integral which forms also part of the approximation in the reference paper. The PEP is then used to evaluate the union upper bound for convolutional codes with Viterbi decoding. Finally, in order to identify the potential of powerful error correction algorithms, like turbo codes as most prominent example in this respect, the lower bound of the error probability is given via the converse of Shannon's coding theorem.
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