communication Networks Another useful manner to evaluate the effectiveness of an FEC that does not need to take into account the receiver parameters is to relate the error probability that would characterize the system without FEC with the error probability of the system with FEC. Generally these error probabilities are called pre-FEC and post-FEC BER. Once the pre-FEC BER is determined the entire system is designed SO as to obtain the wanted pre-FEC BER. After the addition of the FEC, the real error probability is deter- mined by the pre-FEC BER and by the FEC performances. The relation between the pre-FEC and the post-FEC BER is shown in Figure 5.73 for a few BCH codes. As far as turbo codes are concerned, several codes have been constructed with encoder and decoder and analyzed. An example is given in Figure 5.74, where the code gain in terms of SN is shown for three block turbo codes built on RS codes [104]. In particular, the following component codes are selected: Code A: built on RS (15, 12), redundancy 36%, Hamming distance 4 Code B: built on RS (31, 26), redundancy 30%, Hamming distance 6 Code C: built on RS (63, 58), redundancy 15%, Hamming distance 6 From the figure it is evident that the code gain is very high, also for the high redundancy that these codes exhibit, and in particular a code gain a little below 10 dB can be achieved at BER = 10-12. The last observation to be made on the FEC performances is that we have assumed up to now a Gaussian distribution of the decision samples. In reality we will see in Chapter 6 that this is not true: due to the square law detector, when the dominant noise is the ASE noise, the decision samples do not have a Gaussian distribution. w/o code RS 16 BCH 1 BCH 1 (8191,8178) BCH 2 (8191,8165) BCH 2 BCH 3 (8191,8152) (255,247) BCH 3 (255,239) RS 16 (255,223) FIGURE 5.74 Relationship between pre-FEC BER and post-FEC BER for various BCH and RS codes. Technology for Telecommunications: Integrated Optics and Microelectronics It can be demonstrated that, taking into account