noise leads to an alternative definition C' of the channel capacity: (14.36) The new definition of capacity in Eq. (14.36) yields different expressions for the optimal power and maximum capacity, namely Popt and C'max, as defined by: (14.37) (14.38) We note from Eqs. (14.34)-(14.35) and Eqs. (14.37)-(14.38) that the optimal powers Popt, Popt and maximal capacities Cmax, C'max actually have very similar values. With respect to the classical model, the quantum model of the nonlinear channel provides a small correction to the maximum SNR of the order of 2-1/3 2 0.8, which, in base-2 logarithms, represents about 30%. Figure 14.6 shows plots of thee nonlinear-channel capacities C, C' (according to the two above models), as plotted VS. the linear SNR, i.e., SNR = P/N, as expressed in decibels, 19 with different parameter choices for N and Pth. The SHT capacity corre- sponding to the linear-channel case is also shown. Figure 14.6(a) corresponds to the worst case of a channel with a nonlinear threshold relatively close to the linear noise (N = 5 and Pth = 15). In contrast, Figure 14.6(b) corresponds to the case of a compara- tively low linear-noise channel having a relatively high nonlinear threshold (N = 1 and Pth = 100). It is seen from the figure that in both cases, and regardless of the nonlinear model (classical or quantum), the channel capacity is bounded to a power-dependent maximum, unlike in the linear information theory where from SHT the capacity increases as log(SNR). E. Desurvire, Erbium-Doped Fiber Amplifiers, Devices and System Developments (New York: J. Wiley & Sons, 2002), Ch. 3. 19 With SNR(dB) = 10 log 10(SNR). 14.2 Nonlinear channel SNR (dB) SNR (dB) Figure 14.6 Nonlinear channel capacities C, C', , as functions of linear signal-to-linear-noise ratio P/N according to classical and quantum models with SHT linear-channel capacity shown for reference (thick line), with dimensionless parameters (a) N = 5 and Pth = 15, and (b) N = and Pth = 100. The consequences of these developments concerning nonlinear c