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

The capacity and error exponent of the direct detection optical channel are considered. The channel input in a T-second interval is a waveform A(r), 0 5 t I T, which satisfies 0 I A(t) I A, and (l/r)],,%(t) dt I aA, 0 < IT 11. The channel output is a Poisson process with intensity parameter X(t) + he. ‘The quantities A and CIA represent the peak and average power, respectively, of the optical signal, and X0 represents the “dark current.” In Part I the channel capacity of this channel and a lower bound on the error exponent are calculated. An explicit construction for an exponentially opt imum family of codes is also exhibited. 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. DEDICATION These papers are dedicated to the memory of Stephen 0. Rice, an extraordinary mentor, supervisor, and friend. He was a master of numerical methods and asymptotics and was very much at home with the nineteenth-century menager ie of special functions. The generous and easy way in which he shared his genius with his col leagues is legendary, and I was fortunate to have been a beneficiary of his advice and expertise during the first decade of my career at Bell Laboratories. As did all of Steve’s colleagues, I learned much from this gentle and talented man. We will remember him always.