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Block error rate performance of subcarrier intensity modulation based optical wireless communication systems is analysed over Gamma-Gamma and lognormal atmospheric turbulence channels. The analysis is applicable to non-coherent binary modulations and coherent binary phase shift keying. The special cases of K-distributed strong turbulence channel and negative exponential turbulence channel are also considered. The closed-form expressions of block error rate in the Gamma-Gamma turbulence channels are derived using a series expansion of the modified Bessel function. For the lognormal turbulence channels, the Gauss-Laguerre quadrature method can be used to estimate the block error rate accurately.