is- tances, FEC is always used to increase the transmission distance. With standard FEC a post-FEC BER of 10-12 is achieved starting from a pre-FEC BER of about 10-4, that we will take from now on as a second BER reference besides the value of 10-12. The received field after propagation and before the optical filtering that selects the wanted channel can be written in general as follows: (6.54) Transmission Systems Architectures and Performances where the four terms represent in the order information bringing terms (composed by N channels at different wavelengths), the FWM terms (whose number is Nfwm), the XPM terms (whose number is Nxpm), and the ASE noise terms (composed by one noise process for each of the N +2 traversed amplifiers: N along the line plus the preamplifier and the booster). At detection, the optical field is filtered to select the desired channel; this channel is detected by a PIN photodiode and processed by an electronic front end and by a decision circuit to produce an estimate of the transmitted bit stream. The simpler model of the receiver processing chain is shown in Figure 6.19a. As shown in the figure, thermal noise is also added at the receiver, with a process that can be represented like addiction of a white Gaussian noise after the post detection signal amplifier. Carrying out system performance evaluation, using the analog model of the receiver presented in Figure 6.19 is quite difficult; moreover, it does not take into account that in almost all modern receivers, electronics functions are performed via digital circuits after a signal sampling operated immediately after amplification, when the electrical current has a sufficiently high power to correctly feed an A/D converter. Thus, instead of the model of Figure 6.19a, we will assume for the receiver the model in Figure 6.19b. In this model, sampling is performed immediately after the detector amplifier, the ther- mal noise is added as noise over discrete samples, and the analogical integrate and dump circuit that in the analogical m