## 4 Complexity and Performance
### Performance Comparison  
This paper presents an in-depth comparative analysis of key performance indicators, including the average number of LPUs processed during decoding (ANLPU), frame error rate (FER), and bit-error rate (BER). The ANLPU is computed by multiplying the average number of iterations during decoding (ANITER) by the average number of LPUs executed per iteration (ANLPUPTTER). Specific performance indicators for MSB pages, including ANLPUPTTER, ANITER, ANLPU, FER, and BER, measured using LNMS, S-EFB-LNMS, and P-EFB-LNMS LDPC decoding algorithms, are presented in Figures 3-5, respectively. To verify the decoding latency advantage of the proposed algorithms, we present the results for ANITER and ANLPU. Decoding latency is determined by both the codeword length and the number of decoding iterations. When the number of decoding iterations is similar, the decoding latency is comparable [2; 20; 27]. For a single decoding iteration, the decoding latency primarily depends on the number of LPUs executed, where each LPU corresponds to one row of the LDPC matrix \(\mathbf{H}\) in the LNMS LDPC decoding algorithm. Therefore, reducing the total number of LPUs executed during decoding can directly reduce overall decoding latency. Figure 3a,b show ANLPUPTTER and ANITER, respectively. It can be observed that by adjusting parameter \(\beta\), the ANLPUPTTER of the S-EFB-LNMS LDPC decoding algorithm is significantly reduced compared to the LNMS LDPC decoding algorithm [20]. This  
adjustment strategy proves to be effective in optimizing the processing frequency of RLPUs and URLPUs. Although the ANITER slightly increases, as shown in Figure 3b, the overall number of LPUs processed is significantly reduced, as shown in Figure 4.  
Figure 4 compares the MSB page's performance of four different algorithms (LNMS, S-EFB-LNMS:\(\beta=2\), S-EFB-LNMS:\(\beta=3\), and P-EFB-LNMS) in terms of ANLPU across varying PE cycles, ranging from 17,000 to 26,000. ANLPU represents the average number of layered processing units required for decoding, with lower ANLPU values indicating higher efficiency in processing overhead. Across all noise levels, LNMS consistently shows the highest ANLPU values, whereas S-EFB-LNMS and P-EFB-LNMS exhibit significantly lower ANLPU values, especially as noise levels increase. Specifically, as the noise level increases, the ANLPU value of LNMS rises from 847.6 to 5670.6, while P-EFB-LNMS only increases from 511.4 to 2881.1. S-EFB-LNMS also shows a substantial reduction in ANLPU under \(\beta=2\) and \(\beta=3\), with the reductions becoming more pronounced at higher noise levels. These results demonstrate that, compared to the LNMS LDPC decoding algorithm, the S-EFB-LNMS and P-EFB-LNMS LDPC decoding algorithms both significantly improve processing efficiency, particularly under high-noise conditions, by reducing the number  
Figure 4: Average number of LPUs processed during decoding (ANLPU) for MSB pages using LNMS, S-EFB-LNMS, and P-EFB-LNMS LDPC decoding algorithms: \(T=5000\), with PE cycles ranging from 17,000 to 26,000. Lower ANLPU values indicate reduced decoding latency. Figure 3: Performance comparison of LNMS, S-EFB-LNMS, and P-EFB-LNMS LDPC decoding algorithms for MSB pages: \(T=5000\), with PE cycles ranging from 17,000 to 26,000. **(a)** Average number of layered processing units executed per Iteration (ANLPUPTITER). **(b)** Average number of iterations during decoding (ANITER). of processing nodes. The average reductions in the number of LPUs processed for S-EFB-LNMS with \(\beta=2\), S-EFB-LNMS with \(\beta=3\), and P-EFB-LNMS are 21.63%, 20.47%, and 42.49%, respectively, when compared to the LNMS LDPC decoding algorithm. Consequently, the proposed S-EFB-LNMS and P-EFB-LNMS LDPC decoding algorithms achieve a substantial reduction in decoding latency. In addition, the P-EFB-LNMS LDPC decoding algorithm enables the simultaneous updating of the posterior probability through its unique internal design optimization by avoiding address conflicts between RLPU and URLPU.