# A Universal Low-Complexity Demapping Algorithm for Non-Uniform Constellations
## 5 Performance Evaluation
### BER Simulation Results  
According to the description in Section 4, if condensation characteristic is not used, SCSR algorithm can achieve the same performance as Max-Log-MAP algorithm, so the condensation characteristic is the factor that causes the performance difference between SCSR algorithm and Max-Log-MAP algorithm. However, the constellations obtained by the SCSR algorithm and QCSR algorithm after using the condensation characteristic are the same, so the factor that causes the performance difference between the two algorithms is the constellation points contained in subsets. Figure 6 compares the BER performance of the Max-Log-MAP algorithm, QCSR algorithm, and SCSR algorithm over i.i.d Rayleigh channel. 2D-256 NUCs are used in the simulation. Figure 6a shows the BER performance comparison when CR = 2/15. Combined with Table 1, it can be seen that the subsets of the QCSR algorithm contain all 16 constellation points. For the received symbols in a certain quadrant, although some constellation points in the subsets are redundant for LLR calculation, it can ensure that all constellation points that may have the minimum ED with the received symbol are contained in the subsets. The subsets of the QCSR algorithm remove these redundant constellation points. Therefore, the complexity of the SCSR algorithm is lower than that of the QCSR algorithm, but it can achieve the same BER performance as the QCSR algorithm. Moreover, due to the use of condensation characteristic, the performance of these two algorithms is 0.006 dB worse than that of the Max-Log-MAP algorithm. Figure 6b shows the BER performance comparison when CR = 6/15. As described in Section 1, the subsets of the QCSR algorithm are determined based on statistical results, which contain some redundant constellation points, and some constellation points that may have the minimum ED with the received symbol are lost. Therefore, the QCSR algorithm has the worst performance. The subsets of the SCSR algorithm contain all constellation points that may have the minimum ED with the received symbol, so its performance is 0.004 dB better than that of the QCSR algorithm. Then, due to the use of condensation characteristic, the performance of the SCSR algorithm is 0.009 dB worse than that of the Max-Log-MAP algorithm. Figure 6c shows the BER performance comparison when CR = 10/15. For the QCSR algorithm, although some constellation points in its subsets are redundant, the subsets still contain all constellation points that may have the minimum ED with the received symbol. Therefore, the performance of the QCSR algorithm and the SCSR algorithm are the same. Due to the use of condensation characteristic, the performance of these two algorithms is 0.006 dB worse than that of the Max-Log-MAP algorithm. Figure 6d shows the BER performance comparison when CR = 13/15. Since the condensation characteristic cannot be used, the SCSR algorithm has the same performance as the Max-Log-MAP algorithm. And some constellation points that may have the minimum ED with the received symbol are lost in the subsets of the QCSR algorithm, so the QCSR algorithm has the worst performance. The performance of the SCSR algorithm is 0.05 dB better than that of the QCSR algorithm. When using 1D-1024 NUCs, the performance comparison between the SCSR algorithm and the Max-Log-MAP algorithm is shown in Figure 7. Similar to Figure 6, when the condensation characteristic can be used, the SCSR algorithm has a slight performance loss compared with the Max-Log-MAP algorithm. When the CR is 2/15, 6/15, 10/15, the performance of the SCSR algorithm is worse than that of the Max-Log-MAP algorithm by 0.003 dB, 0.004 dB, and 0.0001 dB, respectively. When CR is 13/15, the condensation characteristic cannot be used, so the performance of the SCSR algorithm is the same as that of the Max-Log-MAP algorithm. Figure 6: BER Performance comparison of Max-Log-MAP, QCSR and SCSR algorithms over i.i.d Rayleigh channel. Results presented for 2D-256 NUCs.