## 4 Experiment  
An experiment based on the open-source Polar encoding and decoding code by [PERSON] on GitHub was performed, incorporating an interleaving function and an error detection module into the Successive Cancellation Decoding algorithm. The experimental results are shown in Figure 4; the green line represents the BER of the Successive Cancellation Decoding algorithm without the error detection and correction module, with an information length of 16 and a CRC length of 8, across different SNRs. The red line represents the scheme after the introduction of the error correction mechanism. The experiment we designed is based on the work of [[https://github.com/[PERSON]/PolarCodeDecodersInMatlab](https://github.com/[PERSON]/PolarCodeDecodersInMatlab)]([https://github.com/[PERSON]/PolarCodeDecodersInMatlab](https://github.com/[PERSON]/PolarCodeDecodersInMatlab)) (accessed on 1 May 2023); because this is deeply optimized and accelerated code, it has the best performance compared to the code reproduced by others. The experimental environment is Matlab2022a on the Windows 11 platform, and the computer configuration is as follows: CPU: 13 th Gen Intel(R) Core(TM) i5-13400 2.50 GHz; RAM: 32.0 GB. The experimental samples are randomly generated information bit sequences and Gaussian white noise samples to measure the BLER performance indicators at each signal-to-noise ratio. In addition, we conducted a complexity experiment based on Polar Code, and the experimental results are shown in Figure 5. We also conducted a complexity experiment on the error detection and correction performance of the scheme, and the experimental results are shown in Figures 6 and 7. It can be seen from the complexity experiment that our solution has lower complexity based on Polar Code and can better meet the actual communication efficiency requirements.  
Under different SNR levels, the new Successive Cancellation Decoding algorithm (SC+)--represented by the red line--is compared with the existing algorithm (SC)--represented by the green line--in terms of BLER. Throughout the chart, it is evident that the SC+ scheme consistently exhibits a lower BLER at each SNR point compared to the SC scheme, highlighting its performance advantage.  
Specifically, in the low-SNR region (5 to 7 dB), the new SC+ scheme demonstrates better performance than the existing SC scheme, maintaining a lower error rate even in the presence of weaker signals. For instance, at an SNR of 5 dB, the BLER of SC+ is approximately 0.456, whereas that of SC is 0.424. Although the BLER for both schemes decreases as the SNR increases, the performance improvement of SC+ is more significant at all SNR points.  
In the high-SNR region (9 dB and above), the gap between the SC+ and SC schemes narrows. At an SNR of 9.5 dB, the BLER of SC+ drops to about 0.025, while the BLER of SC is about 0.019, underscoring the clear superiority of SC+ in high-SNR environments.  
In summary, the newly proposed SC+ scheme significantly reduces the error rate across the entire range of SNRs compared to the existing SC scheme, particularly in high-SNR environments, and the algorithm proposed in this paper has the advantage of complexity. This performance enhancement suggests that the SC+ scheme has potential significant value in improving the reliability of communications.  
Figure 4: Comparison of BLER under different SNRs.  
Figure 5: Polar Code complexity experiment.  
Figure 6: Error detection complexity experiment.