## 3 Results and Discussions
The evolution of success probability (SP) for the logic outputs \(O_{1}\) and \(O_{2}\) is analyzed across the parameter space defined by noise strength \(N_{\text{oi}}\) and bit duration time \(T\), as depicted in Figure 6. Figure 6a illustrates that for \(N_{\text{oi}}\) values below 185 dBw, the SP of \(O_{1}\) consistently remains at unity across a \(T\) range of 0.25 ps to 50 ps. Beyond 185 dBw, the SP of \(O_{1}\) falls below unity; however, its anti-noise performance can be significantly improved by increasing \(T\). Figure 6b reveals that for \(T\) values below 8.75 ps, the SP of \(O_{2}\) is less than unity. In the scenario where \(N_{\text{oi}}\) is less than 180 dBw and \(T\) exceeds 8.75 ps, the SP of \(O_{2}\) consistently achieves unity. Nevertheless, as \(N_{\text{oi}}\) surpasses 180 dBw, the SP of \(O_{2}\) exhibits a gradual decline. From the analysis presented, it can be inferred that to ensure error-free operation for both \(O_{1}\) and \(O_{2}\), the bit duration time \(T\) must be set to at least 8.75 ps, and the noise strength \(N_{\text{oi}}\) should be maintained below 180 dBw. This configuration suggests that the maximum operational speed for optical chaotic data selection is approximately 114 Gb/s. Furthermore, the superior anti-noise performance of \(O_{1}\) compared to \(O_{2}\) is attributed primarily to the more pronounced mutual suppression observed between \(\text{x}_{\text{P}}\)-PC and \(\text{y}_{\text{P}}\)-PC as opposed to that between \(\text{x}_{\text{S}}\)-PC and \(\text{y}_{\text{S}}\)-PC, which is illustrated in Figure 5f-i. In summary, it is evident that when the bit duration time \(T\) exceeds 8.75 ps and the noise strength \(N_{\text{oi}}\) falls within the range of 180 dBw to 185 dBw, the logic output \(O_{2}\) may encounter errors, whereas \(O_{1}\) remains error-free. Consequently, by comparing \(O_{2}\) with \(O_{1}\), it is feasible to detect erroneous symbols within \(O_{2}\) and subsequently implement error correction procedures. In this section, we exemplify the system's error detection and correction capabilities by examining noise strengths of 179 dBw, 185 dBw and 190 dBw. The remaining system parameters are consistent with those depicted in Figure 5. At a noise strength of 179 dBw, Figure 7a illustrates that the noise exerts a pronounced effect on the amplitudes of \(\text{x}_{\text{P}}\)-PC, \(\text{y}_{\text{P}}\)-PC, \(\text{x}_{\text{S}}\)-PC and \(\text{y}_{\text{S}}\)-PC. Nonetheless, leveraging the superior mean comparison demodulation mechanism, the logic outputs \(O_{1}\) and \(O_{2}\) exhibit no errors. At a noise strength of 185 dBw, Figure 7b indicates that the logic output \(O_{1}\) remains error-free. Consequently, by comparing it with \(O_{1}\), it is observed that the logic output \(O_{2}\) incurs errors within the time frame of 8.11 ps to 8.16 ps. These errors are indicated with a black solid  
Figure 6: The evolutions of SP in the parameter space of \(N_{\text{oi}}\) and \(T\). (**a**) The SP of logic output \(O_{1}\). (**b**) The SP of logic output \(O_{2}\). line and marked with the symbol 'x'. The corrected logic outputs are depicted by a pink dotted line. When the noise strength is elevated to 190 dBw, as shown in Figure 7c, the logic output \(O_{1}\) encounters errors within the interval of 3.18 ps to 3.19 ps. Similarly, logic output \(O_{2}\) experiences errors in two distinct intervals: 8.1 ps to 8.11 ps and 8.18 ps to 8.19 ps. Thus, under these conditions, both logic outputs are susceptible to errors, leading to the failure of the logic operations.