Capacity of a pulse amplitude modulated direct detection photon channel

The classical direct detection optical channel is modelled by an observed Poisson process with intensity (rate) lambda (t)+ lambda ₀, where lambda (t) is the information carrying input waveform and lambda ₀ represents the \´dark current\´. The capacity of this channel is considered within a restricted class of peak power lambda (t) i, during the ith signalling interval i Delta i) is determined by setting ( lambda _i) to be an independent identically distributed sequence of discrete random variables taking on a finite number of values. The two valued distribution of lambda with mass points located at 0 and A is capacity achieving for sigma =A (no average power constraint) and lambda ₀=0, in the region 0>