# Optical Encoding Model Based on Orbital Angular Momentum Powered by Machine Learning
## 6 Conclusions  
A comprehensive design of an optical encoding model based on the coherent superposition of two \(LG\) beams with OAM is proposed for the generation of a coding system independent of phase information. The proposed approach employs an SVM-ECOC algorithm machine learning that enables image prediction, recognition and classification. To verify the robustness of the proposed optical encoding model, a data symbol code based on a 4-bit data symbol is designed, which is associated with the intensity profile according to the \((p,\ell)\) combination. A channel noise made up of the RIN and AWGN is added to the images generated in the encoding stage to emulate a real environment. In order to identify each data symbol, two different algorithms based on an SVM-ECOC model are used. The efficacy of the proposed approach is validated through BER measurements. The results reveal that the proposed algorithms are able to recognize the data symbol set with a degree of confidence greater than 90 % for noise levels up to 9 dB in both models. Even though both models present high efficiency, the Multicast one-vs-all model (Model 2) presents the best BER curve between the two models studied, with a BER \(=10^{-9}\) for 10.2 dB of SNR. The proposed encoding model can be employed on optical free-space (OPS) data links, which according to the state of the art, such encoding potentially increases data capacity for wireless systems and satellite communication systems [25; 54]. These systems present typical link distances between 1 km and 143 km (verified experimentally), for 532 nm, 633 nm and 1550 nm of operating wavelength and a range between 150 Mbps and 200 Gbps of data rate [11], which complicates the data transmission. However, the proposed optical encoding model can be a solution as it can be used over optical fiber links as evidenced in [25], in which an optical encoding system based on OAM beams has been implemented for data transmission at 80 Gbps using 5 km few mode fibers (FMF) to data transmission at 640 Gbps using 18 km of ring-core-fiber. On the other hand, some constraints must be considered when choosing the type of encrypted data transmission channel. For free-space links, atmospheric turbulence can cause a random phase and intensity distortion on the transversal beam profile [55], which can be quantified by the refractive index structure constant \(C_{n}^{2}\) that has typical values between \(10^{-17}\) m\({}^{-2/3}\) and \(10^{-13}\) m\({}^{-2/3}\). According to [PERSON] et al. [1], the Rytov variance is an adequate indicator to quantify turbulence fluctuations in OFS links, since this is related to \(C_{n}^{2}\) and the propagation distance. Also  
Figure 4: Computed BER for each SVM-ECOC model as a function of SNR for critical noise levels (from 0 to 14 dB). demonstrated in [56], for a link with low power fluctuations (low Rytov variance), the recommended propagation length should be less than 10 km, and for greater distances, the use of mitigation methods such as adaptive optics beam shaping is recommended [57]. Focusing on optical fiber links, the fundamental limitations lie in the type of fiber used for the transmission channel. The use of few mode fibers (FMTs) or the use of micro-structured fibers is necessary to excite OAM modes within the fiber as evidenced in [25]. For future research, it is relevant to mention that the number of circular fringes in the intensity profile of an LG mode are directly related to the index \(p\), while the spatial distribution of these fringes is related to the index \(\ell\); therefore, the number of bits can be extended to more than 4-bits for the case where \(\ell\geq 5\). This fact opens new opportunities for the development of advanced encoding systems. Conceptualization, E.L. and C.S. ; methodology, M.S.A.-A. ; software, C.S. ; validation, A.P., E.L. and P.I. ; formal analysis, E.L.; investigation, C.S; writing--review and editing, E.L. and M.S.A.-A. All authors have read and agreed to the published version of the manuscript.