In this paper, the signal propagation along the fiber, in either absence or presence of the cross talk interference appearing at different places along the fiber, for both dispersive regime cases, is considered. The optical signal that appears at transmitter output has the envelope in super-Gaussian form. The cross talk appears at the transmitter output or along the fiber The pulse shape at the receiver input is determined using Schrodinger equation. The noise sources are the photo detector and resistance in the receiver. The bit error probability of intensity modulation and direct detection (IM-DD) system in the presence of the cross talk, quantum and thermal noise is determined.