Multipulse pulse-position modulation (MPPM) is a preferred signaling scheme for free-space optical (FSO) communications under certain constraints. In order to enable the combination of MPPM with many types of error-correcting codes, it is desirable that the MPPM constellation size is a power of 2. In this paper, we study the selection of MPPM constellations of size 2 k with integer k such that the constellation-constrained channel capacity is maximized. To this end, we consider both the Poisson and the Gaussian regime of the photon detection FSO channel.
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Nguyen et al. (2008) studied this question.