Deep-space optical communication has garnered increasing attention for its high data transfer rate, wide bandwidth, and high transmission speed. However, coronal plasma turbulence severely degrades optical signals during superior solar conjunction. In this study, we introduce the models for plasma density and generalized non-Kolmogorov turbulence power spectrum. Based on these models, we derive the variance of the phase fluctuations with the assistance of the Rytov theory in the weak turbulence regime involving various variables, such as turbulence outer scale, spectral index, relative fluctuation factor, and wavelength. Subsequently, we evaluate the bit error ratio (BER) performance of the deep-space optical communication system, considering phase fluctuations and intensity scintillations, under binary phase shift keying modulation. Numerical calculations reveal that small heliocentric distance, large relative fluctuation factor and spectral index, could induce severe phase fluctuations and high BER. Fortunately, the effects of the plasma irregularities on the BER performance can be mitigated by short optical wavelength under large outer scale.