 6.23 is plotted in Figure 6.16 and shows how S varies with the extinction ratio. For example, the Chapter 6 Optical Fiber Transmission power penalty is less than 1 dB when rex is greater than 8.7. Because extinction ratios are often expressed in decibels, the equivalent value is 9.4 dB. In comparison, ITU-T standards G.691 and G.959.1 for SDH operation at rates from STM-4 to STM-256 recommend minimum extinction ratio values of 6 dB, 8.2 dB, 9 dB, and 10 dB, depending on the system datarate, wavelength range, and transmission span (ITU-T G.959.1). Other Influences on BER Many more results have been derived from the theory of bit error rates that leads to equa- tion 6.23, but it is not possible to reproduce them here. Instead, we comment on some of the BER's main features. The simple analysis that leads to equation 6.21 makes no reference to the effects that cause the statistical variation of the noise currents. There are many con- tributors, but here we mention five terms with their variances: Shot noise, 02 Thermal noise, oth Relative-intensity noise (RIN), Signal-ASE beat noise, O 2 s-ase ASE-ASE beat noise, 02 ase-ase As was explained in an earlier section on amplifier noise, the last two of these apply only if optical amplifiers are used. One of the useful consequences of random independent processes as described by Gaussian statistics is that the total variance of the combined probability density function is the sum of the individual variances (Riley, Hobson, & Bence, 2004). Therefore, in general we have ase-ase (6.24) in which totol can be the total noise variance of a 1 or a 0 bit, as appropriate. Expressions for the terms in equation 6.24 are presented in Steele, Walker, and Walker (1991). As was stated in an earlier subsection on the optical noise figure, shot noise results from the random arrival times of the photons in a stream. The fluctuating photon number translated into shot noise on the photocurrent, which depends on the incident optical power. Thermal noise results from random motion of the elect