# Analysis and Research on Secondary LT Coding Anti-Eavesdropping Scheme Based on LT Code Degree-1
## 4 Simulation Results and Discussion
### Double LT Anti-Eavesdropping Capability Versus the Number of Original Symbols of the Source \(k\)  
In double LT coding, the source symbol \(k\) is chosen to vary from 100 to 1000, and the effect of \(k\) on the decoding overhead \(\varepsilon\) is observed. Other experimental conditions are the same as above. The experimental results are shown in Figure 7.  
From Figure 7, it can be seen that double LT decreases with the increase in \(k\). The experimental results are the same as the theoretical analysis in Section 3.3. Although the \(\varepsilon_{\text{{{{double\_LT}}}}}\) of double LT is larger than the \(\varepsilon_{LT}\) of LT codes, the double LT \(\varepsilon_{\text{{{{double\_LT}}}}}\) for \(k=1000\) is only 1.1427, which can be seen in the lower decoding overhead of long double LT. Variation in the untranslated probability \(P_{\text{{{{Five\_undecode}}}}}\) of Eve is under the variation in channel deletion probability for double LT with different code lengths. If the main channel deletion probability \(P_{AB}=0.3\), \(k\) is chosen to be 2000, 200, and 50, respectively. Observe the effect of the change in the deletion probability of the eavesdropping channel \(P_{AE}\) on \(P_{\text{{{{{Five\_undecode}}}}}}\). The experimental results are shown in Figure 8.  
From Figure 8, it can be seen that under the condition that the main channel \(P_{AB}=0.3\) remains constant, as the eavesdropping channel \(P_{AE}\) increases, the eavesdropper \(P_{\text{{{{Five\_undecode}}}}}\) also grows larger, and at higher \(P_{AE}\), \(P_{\text{{{{Five\_undecode}}}}}\) gradually flattens out and will converge to 1. In the range where \(P_{AE}\) is (0.0.25), the change in \(k\) in the double LT scheme can have a small effect on the eavesdropper \(P_{\text{{{{Five\_undecode}}}}}\), but it also has a certain anti-eavesdropping function. \(P_{AE}\) is (0.25, 0.5), and the eavesdropper's \(P_{\text{{{{Five\_undecode}}}}}\) increases substantially as the source message length \(k\) increases in the double LT scheme. Set the eavesdropping channel deletion probability \(P_{AE}=0.3\), and observe the effect of the main channel \(P_{AB}\) change on \(P_{\text{{{{Five\_undecode}}}}}\). The experimental results are shown in Figure 9.  
Figure 7: Relation curve between \(k\) and \(\varepsilon\). From Figure 9, it can be seen that the eavesdropper's \(P_{\text{eve\_undecode}}\) decreases as the main channel \(P_{AB}\) increases, regardless of what value \(k\) is. \(P_{AB}\) is (0, 0.35), and in the double LT scheme, as \(k\) increases, the eavesdropper's \(P_{\text{eve\_undecode}}\) increases substantially. After \(P_{AB}\geq 0.35\), \(P_{\text{eve\_undecode}}\) begins to decrease as \(k\) increases. The experimental results show that as the source message length \(k\) increases, the RSD has a higher degree-1 probability and a higher number of degree-1 symbols, increasing the secondary LT code source length. LT code uses BP decoding, which can only be decoded by receiving a large enough number of symbols. If Eve receives an insufficient number of symbols to be decoded in the process of BP decoding of LT encoded symbols of degree-1, there exists a large number of degree-1 symbols that can not be decoded, and the next step of BP decoding can not be carried out, resulting in an increase in the untranslated rate. However, when \(P_{AB}\) is slightly larger than \(P_{AE}\), Eve receives a larger number of correctly encoded symbols than Bob, and can decode as long as it receives enough encoded symbols, the advantage of a long double LT is not present, and \(P_{\text{eve\_undecode}}\) begins to decrease as \(k\) increases. Therefore, double LT with a larger number \(k\) of original symbols of the source is suitable to be used more effectively under conditions where the main channel is better or slightly worse than the eavesdropping channel. Figure 8: The effect of a change in the probability of eavesdropping channel deletion \(P_{AE}\) on \(P_{\text{eve\_undecode}}\).