Capacity and error exponent for the direct detection photon channel--Part I.

This is the first of a two-part series on the capacity and error exponent of the direct detection optical channel. The channel input in a T-second interval is a waveform lambda (t), O= t =T, which satisfies O= x(t)= A, and 1 over T integral sup T sub O x(t)dt = sigma A. The channel output is a Poisson process with intensity parameter lambda(t) + lambda (o). The quantities A and sigma A represent the peak an average power respectively of the optical signal and lambda (o) represents the "dark current." In Part I we calculate the channel capacity of this channel and a lower bound on the error exponent. We also exhibit an explicit construction for an exponentially optimum family of codes. In Part II we obtain an upper bound on the error exponent which coincides with the lower bound. Thus, this channel is one of the very few for which the error exponent is known exactly.