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We use a low-density parity-check (LDPC) code to mitigate the effects of fluctuations caused by atmospheric turbulence in an uncorrelated flat free-space optical (FSO) channel. To achieve the threshold close to the FSO channel's capacity, we require an optimum degree distribution for the LDPC codes. We analytically derive the degree distributions of irregular LDPC codes in the gamma-gamma distributed FSO channel by optimizing either SNR or rate. In the SNR-optimized channel, we derive degree distributions for achieving a specific threshold (0.5 dB and 5 dB) at the highest possible rate. In contrast, in the rate-optimized channel, we target a specific rate (0.75 and 0.8) at the lowest possible threshold. For the SNR-optimized case, the maximum achievable code rate decreases from 0.56 to 0.40 at a 5 dB threshold on moving from a weak to a strong turbulence regime. In the rate-optimized case, we obtain the required code rate of 0.8 at the threshold of 11.30 dB and 19.97 dB in weak and strong turbulence regimes, respectively. We report the gap to capacity, which gives how far the LDPC code is operating from the Shannon limit, for these cases, and verify the analytical results by the simulations in MATLAB. This work emphasizes the concept of adaptive coding over the FSO channel.