Maximum achievable throughputs for uncoded OPPM and MPPM in optical direct-detection channels

Tight upper and lower bounds on the maximum throughputs for both overlapping and multipulse pulse position modulation (OPPM and MPPM) in optical direct-detection channels are derived. The corresponding pulse-position multiplicities are estimated. Simple lower bounds for the maximum achievable throughput (with the error rate not exceeding a certain threshold) are obtained for OPPM. A comparison between the maximum achievable throughputs for both OPPM and MPPM is also considered. Our results suggest using MPPM for high efficient transmission and OPPM for low efficient transmission. Namely, MPPM should be used when the transmission efficiency exceeds 0.027 nats/photon.