n of the signal is 3 dB less, giv- ing an S/N value of 18 dB in both repeaters and the error rate at both repeat- ers would be 1 X 1-8. This means that one error occurs on average after 100,000,000 correct bits. Now we have two repeaters and we have an overall error rate of 2 X 10-8 because each of them creates on average one error in each sequence of 1 X 108 bits. We can see that the improvement of 3 dB in the S/N that we achieved with the help of the new repeater reduces the number of errors by a factor of 0.001. Transmission In practice, the error rate of an operational transmission system is often much better and we have close to error-free transmission and the exact equivalent of the original signal is received in the end regardless of the dis- tance (the number of repeaters). The error rate decreases rapidly with noise as shown in Figure 4.19 because of the Gaussian nature of thermal noise. Not only thermal, but many other types of noise in real-life systems are assumed to follow a Gaussian dis- tribution. With this model the reduction of noise by 1 dB improves the error rate by factor of 10 or more, as seen in Figure 4.19. The digital transmission systems installed in telecommunications networks are designed in such a way that noise is low enough in all regenerators and the error rate is extremely low. For example, optical line systems usually have a design practice of worst-case lifetime error rate of 1 X 10-10. In normal operational conditions the error rate is several orders of magnitude better and they operate nearly error free. From the error rate curve in Figure 4.19 we see how the error rate depends on the S/N. From the error rate we can easily calculate the mean time between errors when the data rate is known. Table 4.2 gives examples of error rates and mean times between errors for a 64-Kbps (ISDN B-channel) data channel. Digital systems have a certain threshold value for the S/N. From the curve in Figure 4.19 and Table 4.2, we find that if the S/N is worse than 18 dB, errors occur quite frequentl