Capacity and cutoff rate of overlapping multi-pulse pulse position modulation (OMPPM) in optical direct-detection channel: quantum-limited case

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), multipulse 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.