Cutoff rate of m-ary PPM is derived for an avalanche photodiode (APD) based receiver. The cutoff rate is compared among m=8-256 under the condition of the same total signal energy in 256 slots, where the effects of the timing jitter and atmospheric turbulence are included. Numerical results are shown for the illustrative examples of the cutoff rate.

Cutoff rate of overlapping multi-pulse pulse position modulation (OMPPM) is analyzed in the quantum-limited and the background noise cases. Our results suggest that the derived cutoff rate is higher than conventional one because of the infinite quantization at the demodulator and the definition of the erasure event in conventional analysis.

We analyze the effect of overlapping technique on differential pulse position modulation (DPPM) in optical direct-detection channel when the pulsewidth and the average power of the channel are constrained. We refer to the modulation scheme employing an overlapping technique in DPPM as differential overlapping PPM (DOPPM). To avoid frame synchronization problems, we analyze the performance of DOPPM under the window scheme that results in lower bounds on the capacity and the cutoff rate of DOPPM but is easy to analyze. Under this scheme, we analyze the lower bounds on the capacity and the cutoff rate of DOPPM. It is shown that DOPPM with the window scheme has higher capacity and cutoff rate than PPM and DPPM, and also than OPPM when the average received number of photons per slot is somewhat large. The overlapping technique is thus shown to be effective on DPPM under the pulsewidth constraint when the average received number of photons per slot is somewhat large.

Overlapping multi-pulse pulse position modulation (OMPPM) is a modulation scheme having higher capacity and cutoff rate than other conventional modulation schemes when both off-duration between pulses shorter than a laser pulsewidth and resolution better than a laser pulsewidth are realized [1],[2]. In Refs. [1],[2] erasure events of a few chips that can be decoded correctly is defined as an erasure event. This results in lower bounds on the performance of OMPPM in optical-direct-detection channel in quantum limited case. This paper analyzes more exact performance of OMPPM in optical direct-detection channel in quantum limited case when both off-duration between pulses shorter than a laser pulsewidth and resolution better than a laser pulsewidth are realized. First we derive the error probability of OMPPM with considering what chips are detected or erased. Then we derive the capacity and the cutoff rate of OMPPM using the error probability. It is shown that OMPPM outperforms on-off keying (OOK), pulse position modulation (PPM), multi-pulse PPM (MPPM), and overlapping PPM (OPPM) in terms of both capacity and cutoff rate for the same pulsewidth and the same duty cycle. Moreover, it is shown that OMPPM with fewer slots and more pulses per block has better cutoff rate performance when the average received power per slot is somewhat large.