## 5 Simulation--Results  
Initially, we add the nomenclature table of the parameters used, which can be found in Table 1.  
For our simulations, the AFF3 CT toolbox [44] is used, which is a toolbox dedicated to FEC or channel coding. It is written in C++ and it supports a large range of codes including the new POLAR codes. Here, we will compare the RS codes with the POLAR codes, in order to show metrics such as the BER, Frame-Error-Rate (FER), and throughput. TheAFF3 CT comes with a simulator that is used for communication chains and targets channel coding levels. It is based on a Monte Carlo method, whereby the transmitter emits frames with random noise by the channel and the receiver attempts to decode the noised frames. The transmitter keeps on emitting frames until it reaches a number of errors that is fixed. A frame error takes place when the initial frame from the transmitter is different from the decoded frame of the receiver. This results in the number of simulated frames increasing, in conjunction with the simulation time, when the Signal to Noise Ratio (SNR) decreases.  
The AFF3 CT simulator works from the command prompt and can take a variety of arguments. Here, we selected a number of the available ones, in order to proceed with an initial simulation of the codes. We used the -C argument, which takes as input the type of FEC codes we will use; in our case RS and POLAR. The argument -K is the number of information bits we set to 1723 and -N is the frame size (bits transmitted over the channel) we set to 2047. This gives us the bit rate as well, which is the division between 1723 and 2047, which gives us the value of 0.8417. The AFF3 CT simulator estimates the BER and the FER for an SNR range. The argument -m is the minimal noise energy value (0 dB) to simulate and -M is the maximal noise energy value (4.5 dB). The argument -s is the step between each SNR value we set to 0.5 dB. We also use the -chan-type with the value Additive white Gaussian noise (AWGN). Finally, we use the Phase Shift Keying (PSK) modulation at the modem level. For the simulation, we utilised the standard BER/FER standard [45], which we can see in Figure 4. The complete set of arguments that have been used in this simulation can be seen in Figure 5.  
Thereafter, a simulation of the RS vs. the POLAR codes was performed, and the results were determined with respect to the BER, FER, and throughput that have been exhibited. The reader can see the results in Figures 6-8. In terms of the BER (Figure 6), we can see a decrease in both RS and POLAR codes as the SNR increases. However, the BER of the  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Explanation** \\ \hline -C & input the type of FEC codes we will use \\ -K & number of information bits \\ -N & frame size \\ -m & minimal noise energly value (dB) \\ -M & maximum noise energy value \\ -s & step between SNR value \\ -chan-type & Additive White Gaussian Noise value \\ \hline \hline \end{tabular}
\end{table}
Table 1: Nomenclature.  
Figure 4: Standard BER/FER chain.  
RS codes shows a smoother decrease starting close to 0.7 and ending o 0.147. On the other hand, the POLAR codes commence close to 0.9 BER when the SNR is 1.0 dB, and it ends up to 0 when the SNR is 4.5 dB. In terms of the FER Figure 7, the RS codes exhibit a stationary value ot 1.0 FER throughout the simulation experiment. On the contrary, POLAR codes show a rapid decrease from 1.0 FER to 0.0 FER when the SNR is 4.5 dB. Lastly, as for the throughput, the RS codes show a stable value close to 5 MB/s, while the POLAR codes exhibit a rapid increase from below 4 MB/s at the start to over 10 MB/s at the last value of the SNR.  
Figure 5: POLAR and RS simulation arguments.  
Figure 6: BER of different SNR values for RS and Polar codes.  
Overall, the reader can see that the POLAR codes produce smaller BER and FER with the increase of the SNR value in simulation and higher throughput, which essentially makes them better for the application we are interested in.