Square Root Approximation to the Poisson Channel

Starting from the Poisson model we present a channel model for optical communications, called the Square Root (SR) Channel, in which the noise is additive Gaussian with constant variance. Initially, we prove that for large peak or average power, the transmission rate of a Poisson Channel when coding and decoding methods for the SR Channel are used, converges to the capacity of the Poisson Channel. Then, we derive bounds and asymptotic expressions for the capacity of the SR Channel, and compare them to those of other optical channel models. Finally, signal-independent noise sources are discussed.