# Improving Decodability of Polar Codes by Adding Noise
## 5 Simulation Results
Figure 5: FER performance of the (1024, 512) polar code with different decoding algorithms. The SSC algorithm is in [14], the PB-SSC algorithm is in [33], and the PP-SSC algorithm is in [35]. with other decoding algorithms for the rate-\(3/4\) polar code, respectively. We also see that the proposed decoding algorithms have better error correction performance than other decoding algorithms when the code rate increases. In Figure 6, when SNR = 6.0 dB, we can see from the figure that our proposed Online-PDNE decoding algorithm can improve the BER performance by more than four orders of magnitude compared with the SSC algorithm, more than three orders of magnitude compared with the PB-SSC algorithm and the PP-SSC algorithm. As can be seen from Figure 7 that when SNR = 6.0 dB, the proposed Online-PDNE decoding algorithm improves the FER performance by more than three orders of magnitude compared with the SSC algorithm and more than two orders of magnitude compared with the PB-SSC algorithm and PP-SSC algorithm. Note that compared to the proposed PDNE decoding algorithm, the SNE decoding algorithm significantly reduces the decoding  
Figure 6: BER performance of the (1024, 768) polar code with different decoding algorithms. The SSC algorithm is in [14], the PB-SSC algorithm is in [33], and the PP-SSC algorithm is in [35]. Figure 7: FER performance of the (1024, 768) polar code with different decoding algorithms. The SSC algorithm is in [14], the PB-SSC algorithm is in [33], and the PP-SSC algorithm is in [35]. complexity with negligible performance degradation, which coincide with the results in Figures 4 and 5. In Figures 8 and 9, we compare the average normalized complexities of the proposed Online-PDNE decoding algorithm, the proposed PDNE decoding algorithm, the SNE decoding algorithm and other decoding algorithms for polar codes with two rates, respectively. The average normalized complexity of these algorithms is normalized by the SSC decoding algorithm. It can be observed that the average normalized complexity of the proposed PDNE decoding algorithm and SNE decoding algorithm is much lower than that of the PP-SSC decoding algorithm, which is due to the offline training. Among the proposed decoding algorithms, the online-PDNE decoding algorithm has the best error correction performance and the highest complexity, but it is still much less complicated than the PP-SSC decoding  
Figure 8: The average normalized complexities for the (1024, 512) polar code. The SSC algorithm is in [14], the PB-SSC algorithm is in [33], and the PP-SSC algorithm is in [35]. Figure 9: The average normalized complexities for the (1024, 768) polar code. The SSC algorithm is in [14], the PB-SSC algorithm is in [33], and the PP-SSC algorithm is in [35]. decoding algorithms were proposed. While ensuring the error correction performance, the complexity is reduced by employing the offline neuro-evolution. In addition, it is worth mentioning that the proposed decoding algorithms can be extended to other channel codes in a straightforward manner. As a future work, we plan to apply the proposed decoding algorithms to the polar codes in the 5G standard. Conceptualization, L.K. and H.L. ; methodology, L.K. and H.L. ; software, W.H. and L.K. ; validation, W.H. and L.K. ; formal analysis, W.H. ; investigation, W.H. and B.D. ; resources, W.H. ; data curation, W.H. ; writing--original draft preparation, L.K. ; writing--review and editing, H.L. ; visualization, W.H. and B.D. ; supervision, B.D. ; project administration, L.K. and H.L. ; funding acquisition, L.K. and H.L. All authors have read and agreed to the published version of the manuscript. This research was funded by the JITSF (grant No. jit-b-202110) and the NSFC (grant No. 61871376). Not applicable. The authors declare no conflict of interest.