# Optimized Design for NB-LDPC-Coded High-Order CPM: Power and Iterative Efficiencies
## 7 Simulation Results  
In this section, BER simulations for various schemes with \(\eta=0.5\text{bit}/\text{s}/\text{Hz}\) and \(R=2/3\) are presented. Figure 11 depicts the BER performance of the optimized NB-LDPC code for 8\(M\)2 RC with various inner iterations at fixed 20 outer iterations. The BER curves using various inner iterations almost coincide within approximately 0.8 dB. This finding indicates that the BER performance at low \(\text{E}_{\text{b}}/\text{N}_{0}\) cannot be improved by increasing the iterations again. Conversely, when the \(\text{E}_{\text{b}}/\text{N}_{0}\) exceeds the convergence threshold into the turbo cliff region, the BER performance significantly improved as the number of inner iterations increases. However, the improved effect was no longer outstanding after five inner iterations, in perfect agreement with the EXIT chart analysis.  
Figure 12 presents the BER simulations of the resulting scheme (8\(M\)2 RC) and other candidate schemes (8\(M\)1 REC and 4\(M\)2 RC) using the proposed methods for \(\eta=0.5\text{bit}/\text{s}/\text{Hz}\) and \(R=2/3\), as well  
Figure 11: Bit error rate (BER) performance of the optimized NB-LDPC code for 8\(M\)2 RC with various inner iterations.  
as their original counterparts with or without extrinsic information operation. In this analysis, \(a\) and \(b\) were set to 0.9 and 0.01, respectively. To ensure a fair comparison, the VN degree distribution was maintained with that of the resulting scheme.  
In Figure 12, the convergence thresholds of all the schemes are reported. The resulting schemes step into the turbo cliff region 0.42 and 0.58 dB earlier and show higher power efficiency compared with 8\(M\)1 REC and 4\(M\)2 RC candidate schemes. The resulting scheme provides an approximately 3.95 dB coding gain compared to the uncoded 8\(M\)2 RC, while achieving approximately 0.5 dB and 0.7 dB advantages over those of 8\(M\)1 REC and 4\(M\)2 RC schemes for the BER of \(10^{-3}\), respectively. The schemes with extrinsic information operation always converge to a smaller BER at the turbo cliff region compared to those without extrinsic information operation and it can achieve approximately 0.1 dB advantages. In addition, Figure 13 shows that these optimized schemes using five inner iterations and \(\varepsilon=1e^{-5}\) have fewer average outer iterations with increasing \(\mathrm{E_{b}/N_{0}}\) and exhibit negligible BER performance degradation with respect to their original counterparts with a total of 140 iterations (seven inner iterations \(\times\)20 outer iterations). These optimized schemes attain a suitable tradeoff of the communication reliability and iterative decoding delay and enhance systematic iterative efficiency.  
Figure 12: BER performance of the resulting scheme and other candidate schemes for \(\eta=0.5\) bit/s\(/\)Hz and \(R=2/3\), as well as their original counterparts with or without extrinsic information operation. The vertical lines represent their convergence thresholds achieved from the EXIT chart. The interleaver length is 1152 symbols.  
Figure 13: Average outer iteration comparison of the resulting scheme and other candidate schemes for \(\eta=0.5\) bit/s\(/\)Hz and \(R=2/3\), as well as their original counterparts with or without extrinsic information operation.