# An Improved Marker Code Scheme Based on Nucleotide Bases for DNA Data Storage
## 6 Simulation Results  
In this section, we compared the error correction performance of the proposed scheme, concatenated watermark code scheme, and concatenated marker code scheme. Moreover, we compared the decoding performance of the proposed INMS algorithm to that of the flooding BP algorithm. We used Microsoft Visual Studio 2019 as the simulation platform. To ensure fairness, three schemes were compared at equal levels of storage efficiency. At any same storage efficiency, the comparison was valid. In our simulations, we compared the bit error rate (BER) performance of the schemes at a storage efficiency of 0.72 (which was determined with LDPC code rates \(R_{L}\), \(D_{M}\), and \(D_{E}\)). A quasicyclic LDPC code with code length of 4544 and code rate of 0.9 was used. In the proposed scheme, suppose that \(D_{M}=4\) and \(D_{E}=18\) (which makes the storage efficiency be 0.72). To guarantee the balance of GC content, \(\{\text{AC}\}\) and \(\{\text{TG}\}\) were selected as the marker bases. In other words, the nucleotide base sequences contained two types of markers, \(\{\text{AC}\}\) and \(\{\text{TG}\}\). Since it is difficult to synthesize long chains exceeding 250 nucleotide bases [14], the long sequence was cut into several segments with a length of 110 bases. We assumed that the maximal number of LDPC decoding iterations \(I_{max}=30\), and the maximal allowed position offset \(\text{Omax}=80\) (according to the length of the segments). Figure 4(a) shows the variation in BER with probabilities \(P_{i}+P_{d}\), at \(\gamma=0.002\). Figure 4(b) shows the variation in BER with parameter \(\gamma\) related to substitution errors at \(P_{i}=0.0005\) and \(P_{d}=0.0065\). Figure 5 shows that the BP algorithm was used in all three schemes. Figure 5 demonstrates that the proposed scheme could achieve lower BER than those of the concatenated marker code scheme and concatenated watermark code scheme in the DNA channel. For example, in Figure 4(b), at \(\gamma=0.004\), the BER of the proposed scheme was about 0.003 lower than that of the concatenated watermark code scheme and about 0.025 lower than that of the concatenated watermark code scheme. Figure 5(a) shows the variation in the BER with probabilities \(P_{i}+P_{d}\), at \(\gamma=0.002\). Figure 5(b) shows the the variation in the BER with parameter \(\gamma\) related to the substitution errors at \(P_{i}=0.0005\) and \(P_{d}=0.0065\). Figure 6 shows a comparison of the performance of the INMS and BP algorithms in the proposed scheme, and the BER performance of the INMS algorithm was approximate to that of the BP algorithm, which verified the effectiveness of the INMS algorithm. In Figure 5(b), the BER of the INMS algorithm was higher than that of the BP algorithm when \(\gamma>0.003\) because the INMS algorithm used approximate replacement in the check node update and thus lost some performance. However, the BER of the INMS algorithm was lower than that of the BP algorithm when \(\gamma<0.003\) because the INMS algorithm achieved a better reduction in the correlation effect among the messages after several iterations. A similar case appeared in [19]. The performance of the INMS algorithm was approximate to that of the BP algorithm in all cases. An appropriate correction factor was selected for the INMS algorithm to obtain the above results. Here, \(\sigma=0.45\), which was obtained with numerous simulations. Combining Figures 5 and 6 obviously shows that BER performance could be significantly improved with several synchronizations. In Figure 4(a), for example, at \(P_{i}+P_{d}=0.005\), the BER at the maximal number of synchronizations \(Sm=3\) was reduced by almost 10 times compared to the BER at \(Sm=1\). At the same time, several synchronizations (i.e., joint