hannels remain to be fully explored. It is important to note that the assumption of channel nonlinearity does not affect the key conclusions of Shannon's (linear) information theory, namely the channel coding theorem and the SHT. Indeed, error-correction codes are used in realistic (nonlinear) optical communication systems to enhance SNR and BER performance. The fact that in these nonlinear optical channels the noise is power-dependent does not affect the effectiveness of such codes. The key conclusion is that the capacity limits imposed by Shannon's information theory still apply, despite the new complexities introduced by channel nonlinearity, which introduces yet another upper bound. It should not be interpreted, however, that nonlinearity defines an "ultimate capacity limit" for optical communication channels, present or future. Indeed, optical fiber design makes it possible effectively to reduce fiber nonlinearity by increasing the fiber core size (referred to as the "effective area"), SO as to decrease the nonlinearity threshold, Pth, and, hence, effectively achieve the operating conditions P Pth (s 0). Furthermore, there exist several types of "countermeasures" and power-SNR tradeoffs to alleviate optical nonlineari- ties, which it is beyond the purpose of this chapter to describe. Overall, the key conclusion Gaussian channel and Shannon-Hartley theorem is that the optical communication channel, albeit nonlinear, can be made to operate as a linear channel, which is, therefore, essentially compliant to the capacity limits set up by Shannon's coding theorem. Exercises 14.1 (M): The signal-to-noise ratio in a continuous channel is SNR = + -12.5 dB. What is the channel capacity? Suggest a Reed-Solomon block code for which the capacity could be approached within approximately one bit. 14.2 (T): Show that the differential conditional entropy reduces after analytical computation to 14.3 (T): Show that the capacity of a Gaussian channel with NRZ/OOK modulation rapidly converges with increasing signal power to the 