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

This is the second 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 (from 0 to T) of x(t)dt = sigmaA. The channel output is a Poisson process with intensity parameter lambda(t) + lambda sub 0. The quantities A and sigma A represent the peak an average power respectively of the optical signal, and lambda sub 0 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.