# DIR-Net: Deep Residual Polar Decoding Network Based on Information Refinement
## 4 Experiments and Results
### Comparison with Other Methods  
#### 4.3.1 Comparison Based on BER  
In this section, (32, 16) polar codes were selected to evaluate DIR-Net. We compared this network with other polar decode methods based on deep learning. In the process of testing, some codewords were generated randomly, and encoding was performed according to the polar encoding rules. To simulate the transmission of information in the channel, different levels of Gaussian white noise were added to the encoded codewords. Then, the codewords were taken as test data with diverse deep learning methods. Among the methods, the DIR-Net method with attention-based denoising and attention-based decoding was denoted as \"dno_dec\". In order to evaluate the decoder performance, we used the DIR-Net method without denoiser as the comparison, which is denoted as \"only_dec\", whereas \"only_fc_dec\" denotes the fully connected decoder proposed in [27], which does not contain a denoiser, and \"fc_dec\" denotes the addition of the attention-based denoiser in our paper to [27]. To further evaluate the performance of the attention-based denoiser and decoder, we compared it with the residual decoder, which was proposed in [29], denoted as \"res_dec\". We additionally compared DIR-Net with the traditional SC and BP algorithms to comprehensively evaluate the performance. We tested the methods at different signal-to-noise ratios, SNR = [0, 1, 2, 3, 4, 5, 6, 7, 8] dB, and the curves are shown in Figure 11.  
Figure 10: The BER performance comparison for different training rates.  
Firstly, we compared only_dec and only_fc_dec, which contained only the decoding network without the denoising subnetwork. As shown in Figure 11, when there was only the decoder, the decoding performance of the AFC decoder was significantly better than that of the fully connected decoder with the same number of layers. This illustrates that the attention mechanism in the AFC units indeed improved the decoding performance of the polar codes. On the other hand, we found that, after adding denoising subnetworks to the decoding algorithm, i.e., \"dno_dec\" and \"fc_dec\", the decoding performance of the network was significantly improved. Meanwhile, we also compared the \"dno_dec\" algorithm with \"rec_dec\", and it can be seen in Figure 11 that the DIR-Net method had better decoding performance due to the addition of the attention mechanism in both the denoiser and the decoder. In addition, the proposed method had a lower BER compared to the conventional SC and BP algorithms.  
In the real communication process, fading is often present in the channel. To evaluate the performance of the DIR-Net method in fading channels, Rayleigh fading was taken as an example to perform a simulation. The same dataset was utilized to train and test the fully connected deep learning decoding method proposed in [28], which was specifically designed to decode polar codes in a Rayleigh fading channel. The BER/SNR curves of the two methods are shown in Figure 12.  
Figure 11: BER performance comparison of different network structures and traditional algorithms.  
Figure 12: BER performance of FC-Decoder and DIR-Net in a Rayleigh fading channel.  
It can be seen in Figure 12 that, after adding Rayleigh fading, the difficulty of decoding was significantly increased. As a result, the bit error rate of the decoding algorithm was much higher compared to when only Gaussian noise was introduced. With the addition of the same Rayleigh fading condition, the decoding performance of the DIR-Net method was significantly better than that of the FC-Decoder, which demonstrates that our proposed DIR-Net may be a strong candidate for resisting Rayleigh fading due to its lower BER.