Capacity and cutoff rate for optical overlapping pulse-position modulation channels

Upper and lower bounds on the capacity and cutoff rate for direct-detection optical overlapping-pulse-position modulation channels are derived. It is shown that these bounds are asymptotically tight, in the sense that the difference between the upper and lower bounds converges to zero as the pulse position multiplicity M and/or the average photon count per pulse Q goes to infinity. The tightness of these bounds for finite values of M and Q is investigated by providing some numerical examples. Orders of magnitude of the rate of convergence of the difference between the bounds are also estimated