## 3 Results and Discussions
Their \(BER\) values, respectively, fluctuate within the following ranges: from 1.02 \(\times\) 10\({}^{-2}\) to 1.22 \(\times\) 10\({}^{-2}\) for \(S_{1}^{{}^{\prime}}(t)\), from 6.1 \(\times\)10\({}^{-3}\) to 7.5 \(\times\) 10\({}^{-3}\) for \(S_{2}^{{}^{\prime}}(t)\), from 3.4 \(\times\) 10\({}^{-3}\) to 6.1 \(\times\) 10\({}^{-3}\) for \(S_{3}^{{}^{\prime}}(t)\), and from 7.1 \(\times\) 10\({}^{-3}\) to 9.2 \(\times\) 10\({}^{-3}\) for \(S_{4}^{{}^{\prime}}(t)\). Within this \(k_{inj}\) range, all four decoded messages demonstrate minor oscillatory fluctuations in their \(BER\)s. The \(BER\)s cap at 1.5 \(\times\) 10\({}^{-2}\) for \(S_{1}^{{}^{\prime}}(t)\) and at 8.7 \(\times\) 10\({}^{-3}\) for \(S_{2}^{{}^{\prime}}(t)\), while those for \(S_{3}^{{}^{\prime}}(t)\) and \(S_{4}^{{}^{\prime}}(t)\) do not surpass 3.4 \(\times\) 10\({}^{-2}\)  
Figure 7: Temporal trajectories of the delayed encoding messages, the delayed chaos masked messages, and the decoding messages in the reservoir computing system. Here, (**a1**) the delayed encoding message \(S_{1}(n\!-\!L_{Gx})\) via time step \(n\); (**a2**) the delayed chaos masked message \(U_{Gx}(n\!-\!L_{Gx})\) via time step \(n\); (**a3**) the decoding message \(S_{1}^{{}^{\prime}}(n)\) via time step \(n\); (**a4**) \(S_{2}(n\!-\!L_{Gy})\) via time step \(n\); (**a5**) \(U_{Gy}(n\!-\!L_{Gy})\) via time step \(n\); (**a6**) \(S_{2}^{{}^{\prime}}(n)\) via time step \(n\); (**a7**) \(S_{3}(n\!-\!L_{Ex})\) via time step \(n\); (**a8**) \(U_{Ex}(n\!-\!L_{Ex})\) via time step \(n\); (**a9**) \(S_{3}^{{}^{\prime}}(n)\) via time step \(n\); (**a10**) \(S_{4}(n\!-\!L_{Ey})\) via time step \(n\); (**a11**) \(U_{Ey}(n\!-\!L_{Ey})\)via time step \(n\); and (**a12**) \(S_{4}^{{}^{\prime}}(n)\) via time step \(n\). and 9.5 \(\times\) 10\({}^{-3}\), respectively. Based on findings from earlier studies [28; 29; 30], a \(BER\) that closes at or below 0.01 is indicative of potentially high-quality data transmission within an optical chaos communication framework. As depicted in Figure 2\(c\), when demodulated through correlation and refined by various digital signal processing methods, four distinct baseband signal sets (or bitstreams) encapsulated within the decoded messages \(S_{1}^{{}^{\prime}}(t)\), \(S_{2}^{{}^{\prime}}(t)\), \(S_{3}^{{}^{\prime}}(t)\) and \(S_{4}^{{}^{\prime}}(t)\) are successfully reconstructed. Consequently, the \(BER\) ranges for these retrieved baseband signals (\(b_{1}^{{}^{\prime}}\), \(b_{2}^{{}^{\prime}}\), \(b_{3}^{{}^{\prime}}\) and \(b_{4}^{{}^{\prime}}\)) remain constant and effectively zero, irrespective of \(k_{inj}\) and \(k_{f}\) variations. Figure 10 delves into the performance of the four retrieved baseband signals by presenting their temporal trajectories and eye-diagrams alongside those of the original baseband signals \(b_{1}\)-\(b_{4}\). An inspection of Figure 10 reveals a striking similarity between the temporal profiles of the original signals \(b_{1}\), \(b_{2}\), \(b_{3}\) and \(b_{4}\) and their retrieved counterparts \(b_{1}^{{}^{\prime}}\), \(b_{2}^{{}^{\prime}}\), \(b_{3}^{{}^{\prime}}\) and \(b_{4}^{{}^{\prime}}\), respectively. The eye-diagrams corresponding to the original and retrieved baseband signals also correspond closely, with \(b_{1}\), \(b_{2}\), \(b_{3}\) and \(b_{4}\), showing a remarkable resemblance to \(b_{1}^{{}^{\prime}}\), \(b_{2}^{{}^{\prime}}\), \(b_{3}^{{}^{\prime}}\) and \(b_{4}^{{}^{\prime}}\). Notably, the eye openings in the eye-diagrams for \(b_{1}^{{}^{\prime}}\), \(b_{2}^{{}^{\prime}}\), \(b_{3}^{{}^{\prime}}\) and \(b_{4}^{{}^{\prime}}\) are sufficiently large, which is an important indicator of signal integrity. The insights gathered from Figures 9 and 10 strongly support the effectiveness of our proposed coherent optical chaotic communication system in delivering secure and high-quality data transmission.