# Optimized Polar Codes as Forward Error Correction Coding for Digital Video Broadcasting Systems
## 8 Conclusions  
In this paper, a polar code encoder and decoder are presented. For polar code construction, it has been proven a relation to get the optimized design SNR point required to have the best performance. Moreover, a comparison between optimized polar codes and LDPC code is conducted. Results show that optimized polar codes achieve comparable bit error  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{3}{*}{**Code Rate**} & **BCH +** & **BCH +** & \multirow{3}{*}{**Polar**} & **Polar** & **Encoding** & **Decoding** \\  & **LDPC** & **LDPC** & & **Encoding** & **Decoding** & **Latency** & **Latency** \\  & **Latency (ms)** & **Latency (ms)** & **Latency (ms)** & **Latency (ms)** & **Enhancement** & **Enhancement** \\ \hline
**1/4** & 2.7 & 74.2 & **1.00** & **0.52** & 2.7 & 142.8 \\
**1/3** & 3.9 & 69.8 & **0.98** & 0.59 & 3.9 & 118.0 \\
**2/5** & 4.6 & 62.1 & **0.84** & **0.54** & 5.5 & 115.1 \\
**1/2** & 5.7 & 52.7 & **0.83** & **0.48** & 6.9 & 108.9 \\
**3/5** & 7.2 & 54.1 & **0.82** & **0.51** & 8.7 & 106.9 \\
**2/3** & 7.8 & 49.4 & **0.84** & 0.55 & 9.2 & 90.4 \\
**3/4** & 8.8 & 44.7 & **0.81** & **0.52** & 10.8 & 85.7 \\
**4/5** & 9.4 & 40.5 & **0.84** & **0.51** & 11.2 & 80.2 \\
**5/6** & 8.3 & 37.1 & **0.81** & **0.54** & 10.2 & 66.8 \\
**8/9** & 7.3 & 25.9 & **0.82** & **0.50** & 8.9 & 51.7 \\
**9/10** & 7.4 & 25.0 & **0.82** & **0.47** & 9.1 & 52.6 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Average latency comparisons between (LDPC+BCH) codes and optimized Polar code for normal frame at different code rates \(R\). (bold cells represent the best values).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Code Type** & **Coding Complexity** & **Decoding Complexity** \\ \hline
**Polar Code** & \(O(N\log_{2}N)\) & \(O(\overline{L}N\log_{2}N)\) \\
**LDPC Code** & \(O\big{(}N+g^{2}\big{)}\) & \(O(i_{max}(N\rho+(N-K)\gamma\ ))\) \\
**BCH Code** & \(O\big{(}t\sqrt{K_{bch}}\big{)}\) & \(O\big{(}t\sqrt{N_{bch}}\big{)}\) \\ \hline \hline \end{tabular}
\end{table}
Table 7: Comparison of computational complexity of coding and decoding of Polar, LDPC, and BCH codes.  
rate performance compared to LDPC code for different code rates, while being free of error floor. Although the encoding latency of polar codes is slightly higher than LDPC codes, however, the overall encoding and decoding latency of polar codes is lower than LDPC codes by at least twenty-five times. Polar code takes advantage of low decoding latency, high throughput and flexibility provided by FA-SCL decoding of polar codes. As a result, in this paper, optimized polar code is proposed to replace the LDPC and the BCH codes in the new standards of DVB systems to enhance their performance in terms of latency and throughput. Finally, a complexity comparison show that polar code complexity is less than (LDPC + BCH) codes, which reduces DVB systems complexity.  
As a future work, the performance of the proposed system can be shown for different channel models. Moreover, a hardware implementation for any DVB system after exchanging the existing encoder/decoder by optimized polar encoder/decoder can be established and field measurements can be presented. Another future research direction, we propose to replace the LDPC channel coding in 5G by optimized polar code to benefit from the low latency and high throughput of polar codes over LDPC as proved in our paper.  
Conceptualization, K.E.-A., R.T.E., S.E.R. and B.A.; methodology, K.E.-A., R.T.E., S.E.R. and B.A.; software, K.E.-A.; resources, K.E.-A.; writing--original draft preparation, K.E.-A.; writing--review and editing, K.E.-A., R.T.E., S.E.R. and B.A.; supervision, R.T.E., S.E.R. and B.A.; All authors have read and agreed to the published version of the manuscript.  
The APC was funded by The Egyptian Satellite Company (Nilesat).  
The authors declare no conflict of interest.