PPM transmission over a photon counting channel: comparison among various transmission formats

A detailed analysis for a variety of transmission formats suitable for photon communication systems is presented. More precisely, starting from the basic orthogonal pulse position modulation (PPM), here assumed as a reference, several alternative modulation schemes are discussed. They can be seen as extensions of the basic format or, equivalently, as particular cases of the most complete alphabet obtained by considering all the possible combinations of high and low levels in a transmission organized over slotted time intervals. The analysis is developed in comparative terms, looking at the three parameters which are usually invoked for performance evaluation, i.e. transmission capacity, cut-off rate and bit error rate. Closed form expressions are given in all the examined cases, stressing the role, as figures of merit, of the transmission efficiency and the bandwidth expansion factor. At a parity of the latter parameter, it is shown that the performance of basic PPM can be improved, even significantly, by resorting to the alternative transmission formats. In particular, they maintain the spectral occupancy within acceptable limits, whereas the bit error rate can be lowered using alphabet puncturation or asymmetric error correcting codes