Capacity and cutoff rate of (M+1)-ary decision rules for noisy M-ary optical PPM channel

The channel capacity C and the cutoff rate R sub o of two (M + 1)-ary decision rules for noisy M slots/symbol optical pulse position modulation (PPM) with ideal photon counting are computed and compared. Also the values of the optimum thresholds needed to minimize the signal requirements are given. With a minor increase in hardware complexity, the symbol by symbol threshold decision rule is shown to be superior to the slot by slot threshold detection and decision rule in two aspects: first, it saves more than 0.5 dB in signal energy for the very noisy cases of more than one noise photon per slot (for low noise cases it also saves signal energy, but a negligibly small amount). Second, it is more robust to variations in the noise level.