al systems, which are all to be developed since only binary systems are covered by today's ITU-T recommendations. Due to these considerations, in all our examples, we will not limit our self to consider 7% redundancy codes, even when binary systems are considered. 5.8.5.5 FEC Performances A great effort of research has been devoted to determine the performances of various FECs in terms of SN gain. In the case of optical systems, the results obtained in the FEC-related literature have to be elaborated due to the particular form of the optical receiver. As a matter of fact, we will see in Chapter 6 that the most important application of FEC is in long-haul and ultra-long-haul systems. In this case the error probability depends on the optical signal to noise ratio (SNo), which is in turn proportional to the optical received power. In general the FEC performances are provided in terms of gain on the SN immediately before decision, which in the optical case is the electrical signal to noise ratio (SN). In order to evaluate the performances in terms of optical gain, we have to link the SNo with the SN using the receiver parameters. Even if this relationship can be derived in a general way, this is not SO significant. The most important cases are the two extreme cases in which there is no optical noise and the receiver noise plus shot noise dominates and the case in which the optical noise dominates. As detailed in Chapter 6, these are the cases of unamplified systems and optically ampli- fied systems. In the first case, assuming as always in practice that the received optical signal can be modeled as a time sequence of coherent states, the overall noise after detection is equal to the variance of the shot noise plus the electronic noise (see Section 5.4). Thus the electrical SN can be written as (5.49) as obviously the SN depends on the square of the optical power; thus a gain of X dB in SN results in a gain of X/2 in terms of optical received power. In the case of dominant optical noise, the SNo can be written in gene