# Optimized Polar Codes as Forward Error Correction Coding for Digital Video Broadcasting Systems
## 5 Simulation Results
### LDPC and Polar Codes Comparison  
In this sub-section, optimized polar code performance is compared with the well-known LDPC code. First, the comparison is only restricted with respect to LDPC code, because it is the main inner error correcting technique for all advanced DVB systems. Table 2 summarizes the simulation parameters for both channel coding techniques. Figures 8 and 9 show the error performance comparison between LDPC used in DVB-S2 standard and optimized polar codes for normal frame (\(N=64\),\(800\)) and short frame (\(N=16\),\(200\)), respectively. The short frame is more efficient for minimum latency interactive applications. From the results, it is concluded that optimized polar codes can achieve a comparable performance to LDPC where the difference of \(E_{b}/N_{0}\) for BER \(=10^{-7}\) in worst case is about \(0.3\) dB. Moreover, optimized polar code has better performance than LDPC for code rate \(5/6\) for short frames, the reason for this performance degradation of LDPC code is due to the method of composition for sparse parity check matrix used in LDPC code, which depends on empirical approaches and iterative algorithms, which is not necessarily optimized for all code rates. On the other hand, Tables 3 and 4 present the measured encoding and decoding average latency comparisons between LDPC code and optimized polar code for normal frame and short frame at QEF selected \(E_{b}/N_{0}\) points for reception conditions of different mentioned code rates. The selected \(E_{b}/N_{0}\) is the first value of \(E_{b}/N_{0}\) at which PER is less than \(10^{-7}\) for both coding techniques at each code rate. It is worth to note that short frame with code rate \(R=9/10\) is not applicable according to DVB-S2 standard, and for that no measured values for it. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Code Type** & **Polar Code** & **LDPC Code** \\ \hline Construction & GA technique & DVB-S2 standard \\ Decoder & FA-SCL & BP horizontal layered \\ Max. List size (\(L_{max}\)) / Max. iterations (\(i_{max}\)) & \(L_{max}=32\) & \(i_{max}=50\) \\ Implementation & Full & AMS \\ Frame size (N\({}^{\prime}\)) & 64,800 & 64,800 \\ Puncturing pattern & yes & No \\ Modern Type & BPSK & BPSK \\ Channel Type & AWGN & AWGN \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters for polar and LDPC codes. Figure 7: Polar code BER versus coefficient of variation \(C_{v}\) for different code rates \(R\). Figure 8: BER versus \(E_{b}/N_{0}\) for LDPC & optimized polar codes for normal frame with \(N=64,800\) and different code rates \(R\) in DVB-S2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Frame Type** & \multicolumn{2}{c}{**Normal Frame (64,800) @ QEF**} & \multicolumn{2}{c}{**Short Frame (16,200) @ QEF**} \\ \hline
**Code rate R** & **LDPC Latency (ms)** & **Polar Latency (ms)** & **LDPC Latency (ms)** & **Polar Latency (ms)** \\ \hline
**1/4** & **0.312** & 0.999 & **0.066** & 0.202 \\
**1/3** & **0.399** & 0.985 & **0.092** & 0.200 \\
**2/5** & **0.442** & 0.836 & **0.109** & 0.201 \\
**1/2** & **0.488** & 0.825 & **0.097** & 0.202 \\
**3/5** & **0.630** & 0.822 & **0.162** & 0.205 \\
**2/3** & **0.553** & 0.845 & **0.134** & 0.203 \\
**3/4** & **0.618** & 0.812 & **0.132** & 0.203 \\
**4/5** & **0.662** & 0.837 & **0.133** & 0.203 \\
**5/6** & **0.673** & 0.815 & **0.148** & 0.204 \\
**8/9** & **0.640** & 0.824 & **0.154** & 0.203 \\
**9/10** & **0.641** & 0.819 & **-** & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Encoding average latency comparisons between LDPC code and optimized Polar code for normal frame and short frame. (bold cells represent the best values). Figure 9: BER versus \(E_{b}/N_{0}\) for LDPC & optimized polar codes for short frame with \(N=16,200\) and different code rates \(R\) in DVB-S2. It is observed from Table 3 that the encoding latency for both channel coding techniques is almost small, and from Table 4 that the decoding latency of polar code is at least twenty-five times less than the decoding latency of LDPC code for both frame types.