Power-efficient modulation schemes such as PPM are widely adopted in deep-space optical communications. In order to achieve multi-gigabit transmission, the usage of large number of time slots in PPM is needed that imposes stringent requirements on system implementation. In this paper, we propose the use of orbital angular momentum (OAM) based LDPC-coded PPM as a means to satisfy high-bandwidth demands of future interplanetary communications while keeping system cost and power consumption reasonably low. Because OAM eigenstates are orthogonal, an arbitrary number of bits/photon can be transmitted. The main challenge for OAM based deep-space communication represents the link between a spacecraft probe and the Earth station because in the presence of atmospheric turbulence the orthogonality between OAM states is not longer preserved. We show that the proposed OAM based LDPC-coded PPM can operate under strong turbulence regime when used in combination with receiver spatial diversity.