# Optical Encoding Model Based on Orbital Angular Momentum Powered by Machine Learning
## 5 Results  
The performance of the proposed optical encoding model is measured in terms of signal degradation due to the addition of noise and the bit error rate (BER) presented by the system. It is known that accuracy and precision of an optical encoder depend on detection method and robustness of the SVM training algorithm used [42; 43]. In this context, to validate the influence of noise on transmission and therefore measure the degree of degradation and signal detection, a combination of RIN and AWGN noises has been used as channel noise for all detection and classification cases. The value of \(\alpha\) for RIN has been established by a factor of 0.5 of the uniform random distribution, while for AWGN the mean \(\mu=0\) and signal-noise ratio (SNR) levels have been established at 36 dB (low), 30 dB (medium) and 24 dB (high) that are typical noise levels in optical communication systems [44; 45]. To understand how the combination of these noises affects the transmitted signal, three different data symbols are presented in Figure 3: 0011 (Figure 3a.i), 0110 (Figure 3b.i) and 1011 (Figure 3c.i) with their corresponding 2D linear transformations of 200 \(\times\) 200 pixels (computational burden), Figure 3a.ii, b.ii and c.ii. With a view to show the impact of the noises in the transmitted signal, the horizontal position arrangement for pixel 50 of the vertical position (x,50) has been chosen for display purposes, which is presented as a yellow dotted line in Figure 3a.ii, b.ii and c.ii. As a result, the normalized intensity curve for such an array is presented in Figure 3a.iii, b.iii and c.iii. Figure 2: Data symbol set based on a 4-bit data symbol for the case study presented. The normalized intensity curves show the original transmitted signal in a black curve, the received signal with the same \(\alpha\) for each case (\(\alpha=0.5\) for RIN) and with low level channel noise in a blue curve, medium level in a red curve and high level in a green curve. The results of Figure 3 reveal that despite observing distortion in the signal due to the addition of noise for levels greater than 24 dB of SNR, the SVM-ECOC model allows each  
Figure 3: Different data symbols and their corresponding normalized intensity curves: (**a.i**) data symbol 0011; (**b.i**) data symbol 0110; (**c.i**) data symbol 1011; (**a.ii,b.ii,c.ii**) linear transformation of (**a.i,b.i,c.i**); (**a.iii,b.iii,c.iii**) normalized intensity curve corresponding to a pixel array of a 2D image (dotted yellow line) with different channel noise levels. image to be correctly classified and recognized, with a percentage of 100 % recovery for each data symbol. For this reason, a computed BER measurement for values less than 24 dB of SNR is necessary to validate the robustness of the optical encoding model at much more critical noise levels. An end-to-end performance measure for data transmission is BER, which quantifies the reliability of an entire coding system from \"input bits\" to \"output bits\", including the behaviour of all components and elements between the transmitted signal and the received signal in addition to considering the path of the signal in the middle [46; 47]. BER is mathematically defined as the relation between the number of bit errors and the total number of bits [48], which expresses the probability of a bit error. The machine learning model for prediction, recognition and classification of images on the receiver side of the proposed optical encoder is based on the SVM-ECOC multicast algorithm, which can be modelled with binary combinations of each class (one-vs.-one) or with binary combinations of one to multiple classes (one-vs.-all) [49; 50], so the BER measurement for each machine learning model becomes a reliable metric of confidence level at the receiving point. To calculate the BER as a function of SNR at the receiver end using the SVM-ECOC model, the training model (one-vs.-one or one-vs.-all) is first created based on the data set of 4-bit symbols (see Figure 2).