# DIR-Net: Deep Residual Polar Decoding Network Based on Information Refinement
## 4 Experiments and Results
### Ablation Experiments  
#### 4.2.1 Denoiser Performance  
As is known, denoising is the preprocessing for codewords before decoding. The noise interference can be effectively reduced by a denoiser, which is convenient for more accurate performance of the decoder. In this section, we explore the effect of the proposed denoisers  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Block** & **Layer** & **Number** \\ \hline Input & \(N\times 1\) & \(\times\) 1 \\ \hline ConvBlock & Conv + LReLU \(k3\)s1 \(N\times 16\) & \(\times\) 1 \\ \hline \multirow{4}{*}{\begin{tabular}{c} AFC \\ Module \\ \end{tabular} } & FC + LReLU 512 \(\times\) 1 & \multirow{4}{*}{\(\times\) 1} \\  & FC + LReLU 256 \(\times\) 1 & & \\ \cline{1-1}  & FC + Sigmoid 512 \(\times\) 1 & & \\ \cline{1-1}  & Multiply 512 \(\times\) 1 & & \\ \hline \multirow{4}{*}{\begin{tabular}{c} AFC \\ Module \\ \end{tabular} } & FC + LReLU 256 \(\times\) 1 & \multirow{4}{*}{\(\times\) 1} \\  & FC + LReLU 128 \(\times\) 1 & & \\ \cline{1-1}  & FC + Sigmoid 256 \(\times\) 1 & & \\ \cline{1-1}  & Multiply 256 \(\times\) 1 & & \\ \hline \multirow{4}{*}{\
\begin{tabular}{c} AFC \\ Module \\ \end{tabular} } & FC + LReLU 128 \(\times\) 1 & \multirow{4}{*}{\(\times\) 1} \\  & FC + LReLU 64 \(\times\) 1 & & \\ \cline{1-1}  & FC + Sigmoid 128 \(\times\) 1 & & \\ \cline{1-1}  & Multiply 128 \(\times\) 1 & & \\ \hline \multirow{4}{*}{
\begin{tabular}{c} AFC \\ Module \\ \end{tabular} } & FC + LReLU 64 \(\times\) 1 & \multirow{4}{*}{\(\times\) 1} \\  & FC + LReLU 32 \(\times\) 1 & & \\ \cline{1-1}  & FC + Sigmoid 64 \(\times\) 1 & & \\ \cline{1-1}  & Multiply 64 \(\times\) 1 & & \\ \hline Output & FC \(\times\) 1 & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Network structure of decoding subnetwork.  
with different code lengths, and we compare the results with the absence of denoising. The denoiser is composed of a convolution layer, which can denoise codes with different lengths without changing the structure. As a result, (16, 8) polar codes were adopted as training data, and (16, 8), (32, 16), (64, 32), (128, 64), and (256, 128) polar codes were utilized as test data in the experiment. The test signal-to-noise ratio (SNR) ranged from 0 dB to 8 dB for different code lengths. The results before and after denoising are shown in Figure 6.  
In Figure 6, the blue line is the SNR of the signal received without denoising. As shown, the convolutional denoiser utilized could achieve denoising for different code lengths. Our denoising network was trained at the code length of (16, 8); thus, the optimal effect was achieved for this code length as we expected. Furthermore, the data with other code lengths were fed into the network for testing. It can be seen in Figure 6 that, even though the denoiser was not trained on these code lengths, the noise could still be removed effectively, mainly benefiting from the local information processing capacity of the convolutional network. Moreover, the denoising effect was obvious when the code length was short. With the increase in code length, although the denoising ability of the denoiser weakened, it could still play a role in noise reduction. The experiment illustrates that the convolutional denoiser we utilized could denoise the received codeword information effectively such that the output result of the decoder was less affected by noise and more accurate.  
The probability density distribution obtained after training with 0 dB of SNR is shown in Figure 7. The green area is the signal not denoised by the denoiser, while the pink area is the signal denoised by the denoiser. When the SNR was small, the codeword information suffered much noise interference. It can be seen from the green area that the signal was submerged by noise. However, after passing through the denoiser, more noise could be removed and the BPSK modulated signal was obtained, indicating that the denoiser could work effectively.  
Figure 6: The SNR comparison of signals before and after denoising with different code lengths.