## 1 Introduction  
The use of machine learning techniques in optical communication networks is currently a popular research topic [1]. Among the various algorithms for machine learning the support vector machine (SVM) can provide a powerful way of learning nonlinear functions. Besides noise, optical data transmission is also affected by linear and nonlinear impairments. Using coherent detection at the receiver, linear effects like chromatic dispersion can be successfully post-compensated by digital signal processing (DSP). Compensation can be done through a finite impulse response filter, also known as feed-forward equalizer (FFE). In case of long transmission distances, a separate electronic dispersion compensation (EDC) [2] is usually implemented, since otherwise too many coefficients for the adaptive FFE structure are required. With an increasing launch power, nonlinear effects additionally occur. For single-carrier transmission self-phase modulation (SPM), caused by the Kerr effect and nonlinear phase noise (NLPN), which results from the interaction between the amplified spontaneous emission (ASE) noise of inline optical amplifiers and SPM can be regarded as the most limiting nonlinear distortions [3]. These impairments cannot be compensated with conventional FFE structures. Previous approaches for the compensation of these nonlinear impairments focused on replacing the FFE by a nonlinear Volterra equalizer (NLVE) [4] or, if the fiber parameters are known, to replace the EDC with a digital backpropagation algorithm to compensate for linear and nonlinear effects simultaneously [5]. After using these methods, a signal detection with conventional linear decision thresholds takes place.  
Another approach for the compensation of nonlinear effects is an extended signal detection where the decision thresholds are adjusted to the disturbed constellations. In other words, the equalization problem is defined as a classification task. To solve this problem suitable algorithms such as expectation maximization (EM) [6; 7], k-means algorithm (KMA) [8; 9], neural network [10] or SVM [11] can be found in the large field of machine learning algorithms.  
The advantage of extended signal detection by SVM is already emphasized in references [3; 12; 13; 14]. In order to investigate exclusively the influence of nonlinearities such as NLPN or SPM, the influence of dispersion has been neglected deliberately in the past [3; 12]. The absence of dispersion means that the interaction between dispersion and nonlinearities is not investigated. Thus, it should be examined whether these equalization techniques work equally well in dispersion influenced transmission.  
In this paper we apply the SVM algorithm to a 64-QAM based coherent optical data center interconnect transmission system to mitigate nonlinear impairments after 100 km transmission distance, including the influence of dispersion. We numerically investigate, for the first time of our knowledge, the impact of different combinations of equalizer (FFE, NLVE) with various detection structures (SVM, KMA). Additionally, we show that the combination of SVM and NLVE can reduce the computational complexity of the NLVE and that this combination allows a more accurate compensation of the impairments that arise in an optical transmission system that is operated in the nonlinear regime.