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In order to achieve multigigabit transmission (projected for 2020) for the use in interplanetary communications, in this letter, we propose the use of multidimensional pulse-position modulation (PPM). From Shannon's theory, we know that information capacity is a logarithmic function of signal-to-noise ratio, but a linear function of number of dimensions. By using pulse-positions as a basis function, we can improve the spectral efficiency of conventional PPM. The N-dimensional PPM (ND-PPM) can, therefore, be used to solve the high-bandwidth requirements of future deep-space optical communications. The N -dimensional signal constellation can be obtained as N-dimensional Cartesian product one-dimensional pulse-amplitude modulation constellation. The improvement of ND-PPM over PPM for N=8 in strong turbulence regime is even 3.21 dB at a bit-error rate (BER) of 10-5. In addition, the spectral efficiency of the proposed scheme is N/log2N times better than that of PPM.