Transmission efficiency in photon counting channels

An investigation is presented of the maximum transmission efficiency that can be reached over an ideal photon counting channel, having fixed the bandwidth expansion factor. First, the ideal situation, represented by C.E. Shannon´s (1959) theorem for discrete channels, is analyzed. A low average number of photons per pulse is demonstrated to be preferable. A binary transmission, with different a priori probabilities of the two transmitted symbols, exhibits a higher efficiency than that of an orthogonal PPM (pulse-position modulated) transmission, whose M-ary symbols are equiprobable, for an equal bandwidth expansion. Then practical transmissions are considered. The PPM technique can be very efficiently coded, and in some situations, is characterized by a bit error probability lower than that of the uncoded binary technique. However, uncoded binary transmission remains extremely attractive for the achievement of ultrahigh transmission efficiencies