## 4 Simulation Results and Discussions  
In this section, we compare the performance of the ALF decoder, the D-SCLF decoder, and the CA-SCL decoder. The default value of \(z\) for our new flip metric is 5. The order of the list flip decoders is 2 for comparing the high-order error-correction capacity. The AWGN channel, BPSK modulation, and the GA construction algorithm with a fixed \(E_{b}/N_{0}\) of 4 dB are used. The generator polynomial of the 24 CRC bits is \(g(x)=x^{24}+x^{23}+x^{6}+x^{5}+x^{1}+1\). To further verify whether our simplified flip metric is still valid with different code rates, we plotted Figures 6 and 7, which show the comparison of the performance of the D-SCLF2 decoder using the original flip metric and the D-SCLF2 decoder using the simplified flip metric for different code rates. In these figures, solid lines represent the performance of the D-SCLF2 decoder using our simplified flip metric, and dotted lines represent the performance of the D-SCLF2 decoder using the original flip metric. \(L_{max}=4\). the average complexity of the D-SCLF2 decoder using the adaptive list is significantly lower than that of the original D-SCLF2 decoder at \(FER=10^{-3}\), which means that the introduction of the adaptive list greatly reduces the complexity of the D-SCLF2 decoder at a high SNR. Therefore, the simulation results are consistent with the theoretical analyses in Section 3.2. Figure 6: Comparison of the FER performance of the D-SCLF2 with the original flip metric and the D-SCLF2 with the simplified flip metric, for \(PC(512,128+24)\), \(PC(512,256+24)\), and \(PC(512,384+24)\). Figure 7: Comparison of the average complexity performance of the D-SCLF2 with the original flip metric and the D-SCLF2 with the simplified flip metric, for \(PC(512,128+24)\), \(PC(512,256+24)\), and \(PC(512,384+24)\). To compare the performance of our ALF2 decoder and the D-SCLF decoder, we drew Figures 10 and 11, which show the performance comparison of the original D-SCLF2 decoder and our ALF2 decoder for different code rates. In these figures, solid lines represent the performance of our ALF2 decoder, and dotted lines represent the performance of the original D-SCLF2 decoder. Figure 8: Comparison of the FER performance of the D-SCLF2 without an adaptive list and the D-SCLF2 with an adaptive list, for \(PC(512,128+24)\), \(PC(512,256+24)\), and \(PC(512,384+24)\). Figure 9: Comparison of the average complexity performance of the D-SCLF2 without an adaptive list and the D-SCLF2 with an adaptive list, for \(PC(512,128+24)\), \(PC(512,256+24)\), and \(PC(512,384+24)\). Figure 10 shows that our ALF2 has an FER performance similar to that of the D-SCLF2 decoder with the same code rate and \(T\). Moreover, the ALF2 decoder has better FER performance than the D-SCLF2 decoder in some nodes since the accuracy of the original flip metric has room for further optimization. Figure 11 shows a comparison of the average complexity performance of the D-SCLF2 and the ALF2, for \(PC(512,128+24)\), \(PC(512,256+24)\), and \(PC(512,384+24)\). Figure 10: Comparison of the FER performance of the D-SCLF2 and the ALF2, for \(PC(512,128+24)\), \(PC(512,256+24)\), and \(PC(512,384+24)\). We noticed that as \(E_{b}/N_{0}\) is increased, the average complexity of the ALF2 decoder and the DSCLF2 decoder all decrease regardless of the code rate and \(T\) value. In all cases, the average complexity of our ALF2 decoder always decreases faster than the D-SCLF2 decoder. In particular, when \(T=15\) and \(E_{b}/N_{0}=2.5 dB\), our ALF2 decoder can reduce the average complexity of the D-SCLF2 decoder by \(68.35\%\) without losing error-correction performance. To show the complexity performance more clearly, we created Tables 4-6, which show the details of the comparison of the average complexity performance in Figure 11.  
example, as shown in Figure 12, we can use the decoder of the CA-SCL decoder (\(L=32\)) to replace the ALF2 decoder (\(L_{max}=4\), \(T=50\)) or the D-SCLF2 decoder (\(L_{max}=4\), \(T=50\)) when the channel noise is generally large.