Efficient Coding and Mapping in Photon Communication Systems

Abstract

Optical communication using photon-counting techniques is very promising for achieving ultimate sensitivity detection limits. In its basic form, an ideal photon counting channel is characterized by two levels of received signals: the one null (0), the other with λ received photons on average (1). No background noise is assumed to affect the transmission and no additional disturbance is present in the receiver. The statistical properties of photon arrivals are those of a pure Poisson process so that, if we set the decision threshold in the receiver between zero and one photon, the probability that a high transmitted signal is received as a low signal results in p=exp(-λ), while the probability that a low transmitted signal is interpreted by the receiver as a high signal is null. Photon counting, therefore, gives a typical example of asymmetric channel. In order to minimize the bit error rate at the output of the receiver, a classical solution is the adoption of an orthogonal pulse position modulation (PPM)¹, to which a suitable external code is applied. PPM is based on the subdivision of the symbol time duration T_s into q adjacent time slots, so that it can be arranged assigning a high level of transmitted signal to only one time slot per symbol. Owing to the properties of the channel, such an alphabet can suffer the presence of erasures only (and not of errors), so that the application of a Reed-Solomon (RS) code, i.e. a code with powerful capabilities of erasures filling, greatly improves the transmission performance².