nsmission pipe in the channel is free from any power- dependent signal degradation effects. In the physical world, such effects are referred to as nonlinearities. Such nonlinearities are usually not observed in vacuum or atmospheric space. 14 However, they are observed in transmission media such as optical fibers, for instance. The advent of high-speed optical telecommunications in the last 20 years has come with the discovery of various types of nonlinearity, namely, Raman and Brillouin scattering, self-and cross-phase modulation, and four-wave mixing. Such nonlinearities cause power limitations (hence SNR and BER limitations) in fiber-optic systems. In the following, I shall focus on fiber-optic systems as an illustration of the nonlinear communications channel. An optical fiber is a highly transparent transmission medium. However, optical signals are attenuated on propagation therein, according to an exponential law P' AP = P exp(-aL), where L is the fiber length and a the attenuation coefficient. For lengths of km and 100 km, the relative signal attenuation or power loss is typically 90% (a ==0.1) or 99% (A = 0.01) respectively. To compensate for fiber loss, fiber-optic systems use in-line optical amplifiers. Such amplifiers are periodically placed every 50-100 km (depending on applications) to produce a signal gain g = 1/2, such that the At least with the power levels used in telecommunications. The atmosphere is made of atomic and molecular matter, which may exhibit nonlinear absorption or scattering at certain frequencies and powers, and a vacuum is nonlinear from the high-energy physics or quantum-electrodynamics viewpoint. Gaussian channel and Shannon-Hartley theorem signal power at the amplifier output is P' = gAP = P. The amplified fiber-optic link is said, therefore, to be transparent. However, the amplification process produces additive noise, which accumulates linearly along the transparent link, each amplification stage contributing to a noise increment. Overlooking any effect contributed by the op