# The Polar Code Construction Method in Free Space Optical Communication
## 5 Simulation Analysis of Polar Code Construction  
STPO was used to construct polar code by combining UPO with MC. Based on inheriting the general properties of UPO, Monte Carlo was introduced into the strong turbulence channel to compare and analyze the sub-channels whose reliability cannot be determined by UPO. In order to verify the reliability of STOP in constructing polar code sequence in FSO strong turbulence channel, we conducted relevant simulation experiments in the system model which was introduced in Part 2, and the system parameters are shown in Table 7. Then MC and STPO were used to construct polar code, respectively, in the MATLAB simulation environment. When SNR < 5 dB, \(\beta\) value was set to 1.1892, and when SNR > 5 dB, \(\beta\) value was set to 1.1727. Successive cancellation (SC) decoding was selected as the decoding method for the simulation experiment. When the code length was 1024 as shown in Figure 6, the reliability of each sub-channel was given by the STPO structure polar code. When constructing polar code with STPO, sub-channels with a high reliability are selected to carry information bits, and other sub-channels carry frozen bits to complete the construction of the polar code, thus saving a lot of system resources. The BER of the polar code constructed by STPO and MC is shown with different code lengths and different code rates in Figure 7. It can be seen from Figure 7 that when the code length was 512 and the code rate was 0.5, the polar code constructed by STPO had the same BER in low SNR and produced a loss of about 0.03 dB in high SNR, compared with that under the MC method. When the code length increased to 1024 and the code rate was 0.5, STPO still had the same error performance as MC in low SNR, but the loss in high SNR \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{\(N\)} & **Range of \(\beta\) When SNR Is** & **Range of \(\beta\) When SNR Is** \\  & **Less than M-SNR** & **More than M-SNR** \\ \hline
32 & (1.1787,1.2207) & (1,1.1787) \\
64 & (1.1787,1.1939) & (1.1507,1.1787) \\
128 & (1.1845,1.1902) & (1.1676,1.1765) \\
256 & (1.1885,1.1902) & (1.1701,1.1752) \\
512 & (1.1888,1.1895) & (1.1721,1.1735) \\
1024 & (1.1890,1.1893) & (1.1725,1.1729) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The value range of \(\beta\) in different code lengths. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Length of polar code & 512/1024 \\ Code rate & 0.25/0.5 \\ Wavelength & 1550 nm \\ Air fluctuation-distribution & gamma-gamma \\ Transmission distance & 1/3/5 km \\ Modulation & OOK \\ Turbulence intensity & 2.3/3.5/5.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Simulation Parameters. increased to a 0.17 dB loss when BER was \(10^{-4}\). When the code rate was reduced to 0.25, the length was 1024, and the BER of STPO was almost the same as that of MC. Therefore, STPO had an error performance similar to MC with a low bit rate and short code length. When STPO was used to construct polar code, the error performance was improved when the bit length increased and the bit rate decreased. When BER was \(10^{-4}\), the code rate was selected as 0.5; if the code length increased from 512 to 1024, there was a gain of about 0.7 dB; when the code length was 1024, the code rate decreased from 0.5 to 0.25, and there was a gain of about 3 dB. Therefore, in actual optical communication systems, considering the best error performance, the bit rate can be appropriately reduced. In the FSO system, turbulence intensity is an important factor that affects the error code performance. In a strong turbulence channel, the turbulence intensity has a relatively large change. Therefore, atmospheric turbulence has a significant impact on the reliability relationship of the polarized sub-channel.