The Capacity of Avalanche Photodiode-Detected Pulse-Position Modulation

The capacity is determined for an optical channel employing Pulse Position Modulation (PPM) and an Avalanche PhotoDiode (APD) detector. This channel is different from the usual optical channel in that the detector output is characterized by a Webb-plus-Gaussian distribution, not a Poisson distribution. The capacity is expressed as a function of the PPM order, slot width, laser dead time, average number of incident signal and background photons received, and APD parameters. Based on a system using a laser and detector proposed for X2000 second delivery, numerical results provide upper bounds on the data rate, level of background noise, and code rate that the channel can support while operating at a given BER. For the particular case studied, the capacity-maximizing PPM order is near 2048 for nighttime reception and 16 for daytime reception. Reed-Solomon codes can handle background levels 2.3 to 7.6 dB below the ultimate level that can be handled by codes operating at the Shannon limit.