ts generate signal distortion that affects system performances. Moreover, the noise contribu- tion at the receiver is not simply the same Gaussian process whatever bit is transmitted. Different noise processes contribute to the noise and some of them are signal dependent. In this section, we will start to remove some ideal assumption and to confront ourselves with a realistic system performance evaluation. Transmission Systems Architectures and Performances In analyzing a realistic IM-DD system we will always assume that the system is func- tional; thus, all the negative effects have a small impact on system performances and the penalty addition rule can be applied. 6.2.3.1 Evaluation of the BER in the Presence of Channel Memory In a real system, one of the major phenomenon to take into account is fiber propagation. Due to different effects (e.g., chromatic and polarization dispersion and self phase modula- tion [SPM]), there is a pulse spreading during propagation, moving energy between adja- cent bit intervals. This effect has a big impact when energy is moved from a "one" to a "zero," while there is almost no impact if a "one" is adjacent to another "one" or if there is a sequence of "zero." This example shows that in a real system the probability that a bit is detected in the wrong way also depends on the nearby bits. This is called channel memory and has to be taken into account when evaluating system performances. Under the hypothesis of low distortion, we can limit the analysis to patterns of 3 bits, that we will tag with an index = 1, 2,..., 8. The bit in a pattern will be indicated with bkj where j=1, = 2, 3 indicates the bit position and k=1, 2,..., 8 to which pattern the bit belongs. The eight patterns are P1=000;2=100;03=001;Q4=101 Since errors will occur at the receivers, we will distinguish the transmitted pattern, Pk whose bits are tbki and the corresponding pattern estimated at the receiver Pk whose bits are bkj With these definitions, assuming the transmission of uncorrelated and equally probable