Lower bounds on capacity and cutoff rate of differential overlapping pulse position modulation in optical direct-detection channel

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.