## 3 Sources of Stochastic Noises  
There are various sources of stochastic noises in an optical network that affect deterministic non-linearity compensation. The description of the form of stochastic noise in three main sources of long-haul coherent optical system is detailed below:  
1. _Advanced modulation formats_--These have become a key ingredient to the design of modern optically routed networks, as a signal is modulated at amplitude, frequency and phase enabling the information carrying capacity to be doubled. Such signal formats include high-order single-carrier formats (e.g., 16/64-QAM) or multi-carrier modulation schemes (e.g., OFDM) [8] which cope better with 'linear' channel distortions. Unfortunately, high-order signal formats are vulnerable to fiber non-linearities, to the point that, when multiple signals are transmitted spectrally closely to each other the resultant non-linear deterministic noise is so 'dense' that appears stochastic [20; 21]. In multi-carrier modulation schemes such as CO-OFDM, this phenomenon is more prominent due to the high PAPR and the fact that subcarriers are spectrally very close to each other causing inter-carrier interference [8; 20; 21]. 2. _Optical Amplifiers_--In long-range optical communications there is multi-span amplification for keeping the signal power levels high enough, but their excess noise beats with the incoming signal. This noise originates by means of quantum mechanical uncertainties in the number of photons added at each amplifier and ultimately limited by the Heisenberg uncertainty principle [3; 7]. The amplifier excess noise can be interpreted as resulting from unavoidable spontaneous emission into its amplified mode (i.e., ASE). The effect of ASE noise on fiber non-linearity interaction is called parametric noise amplification (PNA). Figure 2: Inverse-Volterra series-transfer function (IVSTF) block diagram for coherent optical orthogonal frequency division multiplexing (CO-OFDM). Where \(m\) is the number of spans in a long-haul network and \(k\) is the Kernel order [13]. (I)FFT: (Inverse) fast Fourier transform. C. _Optical Fibers_--Conventional fibers include SMFs which generally exhibit stochastic noise from polarization rotation. The other form of stochastic noise is due to the interplay between linear CD and Kerr non-linearity when signal-noise interaction is considered. Machine Learning for Fiber-Induced Non-Linear Noise Suppression in Coherent Optical Orthogonal Frequency Division Multiplexing (CO-OFDM)  
MLAs have been widely applied to solve various problems in different areas, such as data mining, pattern recognition, medical imaging, etc., while in telecommunications they have covered a wide range of applications, such as channel modelling and prediction, equalization, demodulation/modulation recognition, and spectrum sensing [18]. MLAs are based on the cross-pollination of optimization theory, statistical learning, Kernel theory and algorithmics. MLAs can predict solutions to a problem when deterministic ones are not feasible. There are three main situations in which MLAs make good candidates:  
1. when closed-form solutions do not exist, and trial and error methods are the only approaches to solving the problem at hand,
2. when the application requires real-time performance, and
3. when faster convergence rates and smaller errors are required in the optimization of large systems. In CO-OFDM, MLAs has indicated [16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36] that stochastic noises can be combated without knowledge of the fiber link parameters. Below we describe the structure of the two main supervised MLAs that have been applied in long-haul CO-OFDM as NLEs, i.e., the ANN and SVM algorithms. It should be noted that for both cases a pseudorandom unrepeated sequence was employed with a length of \(2^{19}-1\) having a period of approximately \(2^{19937}-1\) (Mersenne twister) [46].