# Improving Decodability of Polar Codes by Adding Noise
## 5 Simulation Results  
In this section, the performance of the proposed decoding algorithms is evaluated on a BPSK-modulated additive white Gaussian noise (AWGN) channel, in which the SSC decoder is employed for the standard polar decoding. However, it can easily be extended for other decoding algorithms. In the simulations, we use the same polar codes from [10] with code rates 1/2 and 3/4, and both codes have length N = 1024. The parameters and related values used in the training process are shown in Table 3.  
Figures 4 and 5 illustrate the BER and the FER performances of the rate-1/2 polar code with the proposed decoding algorithms, the SSC algorithm [14], the PB-SSC algorithm [33], as well as the PP-SSC algorithm [35], respectively. As shown in Figure 4, the performance of the proposed three decoding algorithms is better than that of the other algorithms. The performance of the proposed Online-PDNE decoding algorithm is about 1.0 dB, 0.6 dB and 0.5 dB superior to that of the conventional SSC algorithm, the PB-SSC algorithm, and the PP-SSC algorithm at the BER of \(10^{-5}\), respectively. When SNR = 3.5 dB, we can see from the figure that our proposed Online-PDNE decoding algorithm can improve BER performance by nearly four orders of magnitude compared with the SSC algorithm, nearly three orders of magnitude compared with the PB-SSC algorithm, and more than two orders of magnitude compared with the PP-SSC algorithm. In addition, among the three proposed decoding algorithms, the Online-PDNE decoding algorithm has the best performance, followed by the PDNE decoding algorithm. The reason why the Online-PDNE decoding algorithm has the best performance is that the directed neural-evolutionary noise is generated online by the GA process for the uncorrectable sequence, which converts the received signal into the error correction region of its decoding space more accurately. Since the PDNE decoding algorithm and the SNE decoding algorithm use the offline GA process to generate the directed neural-evolutionary noise, the decoding complexity and delay are greatly reduced compared with the Online-PDNE decoding algorithm. However, due to the limitation of the size of the directed noise set and uncorrectable error codewords not encountered during offline training, their performances suffer slightly. Compared with the PDNE decoding algorithm, the performance of the SNE decoding algorithm decreases \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Maximum number of the perturbed attempts T\({}_{1}\) & 10 \\ Maximum number of generations T\({}_{2}\) & 100 \\ Number of individuals in the population T & 10 \\ Crossover probability P\({}_{\text{c}}\) & 0.8 \\ Mutation probability P\({}_{\text{m}}\) & 0.1 \\ Cardinality T\({}_{\text{s}}\) of the set S\({}_{n}\) & 10 \\ Variance of the perturbed noise Q\({}_{\text{p}}\) & 0.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters of the training process. slightly, about 0.2 dB, but its decoding complexity and delay are the lowest, and it only depends on the directed neural-evolutionary noise of offline training to decode correctly. From Figure 5, it can be seen that our proposed three decoding algorithms achieve better performance than the others. This conclusion agrees with the results in Figure 4. When SNR = 3.5 dB, we can see from the figure that our proposed Online-PDNE decoding algorithm can improve FER performance by three orders of magnitude compared with the SSC algorithm, more than one order of magnitude compared with the PB-SSC algorithm and the PP-SSC algorithm. To further evaluate the error correction performance of the proposed decoding algorithms as described in Section 3, we also simulate the rate-3/4 polar code. In Figures 6 and 7, we compare the BER and FER performances of the designed decoding algorithms  
Figure 4: BER 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].