The goal of the Deep Space Optical Communications project at the Jet Propulsion Laboratory is to demonstrate laser communication links at ranges out to approximately 3 AU. In this paper, we discuss a downlink receiver concept capable of demodulating optical pulse-position modulated (PPM) waveforms with data rates varying from approximately 50 kbps up to 265 Mbps, using a range of PPM orders, slot widths, and code rates. The receiver operates on recorded timestamps corresponding to the times-of-arrival of photons detected by a photon-counting detector array followed by a commercial time-tagger. Algorithms are presented for slot, symbol, and frame synchronization as well as parameter estimation. Estimates of link performance are evaluated through Monte- Carlo simulation for an optical channel that includes optical losses, detector blocking, signal clock dynamics, and pointing-induced downlink fades. Based upon these simulation results, it is expected that link closure may be achieved with at least 3 dB of margin under a variety of relevant conditions.