 is a statisti- cal operation prone to errors. The point-to-point system performance is generally measured by the probability that detection fails in identifying a symbol, which is called symbol error probability. If the alpha- bet from which the symbols are taken is binary (i.e., there are only two symbols, "1" and "0"), generally this probability is simply called "error probability" or bit error rate (BER). International standards fix a required error probability that depends on the application, SO that systems have to be designed to reach such reference BER [5,6]. In the case of long-haul and ultra-long-haul transmission, the reference BER is 10-12, and we will use this value every time this will be needed. Frequently, it is interesting to know the degradation introduced in the system perfor- mances with respect to an ideal case by a certain phenomenon; for example, what is the degradation introduced by chromatic dispersion? Transmission fiber sites Demux FIGURE 6.2 Block scheme of a WDM transmission system. Telecommunication Networks In this case, the degradation is measured through the increment with respect to the ideal case of the received power or of the ratio between the received power and noise (called signal-to-noise [SN] ratio) needed to reach the reference BER: this difference is called penalty. In a regime of small effect of the nonideal elements, penalties are frequently added together like independent perturbations. This procedure is justified by the assumption that, in a regime of small perturbation, the relation between the BER and the SN ratio does not change and that the dependence of the SN on the perturbation parameters can be linearized. Let us imagine that in ideal conditions, the BER has the following expression: BER=e-SNi (6.1) SN; being the ideal SN ratio both when a 1 is transmitted and when a 0 is transmitted. Let us also assume that a practical system experiments two impairing phenomena char- acterized by two parameters A and B (e.g., chromatic dispersion and polarization mode disper