Information rates of hard-decision Photon-Limited ppm channels

In this paper, we derive the information rate of hard-decision photon-limited continuous PPM channels. The proposed hard-decision scheme, requiring only the first photoelectron emission instant for demodulation, is much simpler than its soft-decision counterpart previously studied in the literature. We analytically compare the information rates per PPM pulse for these two methods and affirm that the hard-decision loss is no more than 0.834 bit.