With the informationization of social processes, the amount of related data has greatly increased, making traditional storage media unable to meet the current requirements for data storage. Due to its advantages of a high storage capacity and persistence, deoxyribonucleic acid (DNA) has been considered the most prospective storage media to solve the data storage problem. Synthesis is an important process for DNA storage, and low-quality DNA coding can increase errors during sequencing, which can affect the storage efficiency. To reduce errors caused by the poor stability of DNA sequences during storage, this paper proposes a method that uses the double-matching and error-pairing constraints to improve the quality of the DNA coding set. First, the double-matching and error-pairing constraints are defined to solve problems of sequences with self-complementary reactions in the solution that are prone to mismatch at the 3\' end. In addition, two strategies are introduced in the arithmetic optimization algorithm, including a random perturbation of the elementary function and a double adaptive weighting strategy. An improved arithmetic optimization algorithm (IAOA) is proposed to construct DNA coding sets. The experimental results of the IAOA on 13 benchmark functions show a significant improvement in its exploration and development capabilities over the existing algorithms. Moreover, the IAOA is used in the DNA encoding design under both traditional and new constraints. The DNA coding sets are tested to estimate their quality regarding the number of hairpins and melting temperature. The DNA storage coding sets constructed in this study are improved by 77.7% at the lower boundary compared to existing algorithms. The DNA sequences in the storage sets show a reduction of 9.7-84.1% in the melting temperature variance, and the hairpin structure ratio is reduced by 2.1-80%. The results indicate that the stability of the DNA coding sets is improved under the two proposed constraints compared to traditional constraints.

Synchronization (insertions-deletions) errors are still a major challenge for reliable information retrieval in DNA storage. Unlike traditional error correction codes (ECC) that add redundancy in the stored information, multiple sequence alignment (MSA) solves this problem by searching the conserved subsequences. In this paper, we conduct a comprehensive simulation study on the error correction capability of a typical MSA algorithm, MAFFT. Our results reveal that its capability exhibits a phase transition when there are around 20% errors. Below this critical value, increasing sequencing depth can eventually allow it to approach complete recovery. Otherwise, its performance plateaus at some poor levels. Given a reasonable sequencing depth (≤ 70), MSA could achieve complete recovery in the low error regime, and effectively correct 90% of the errors in the medium error regime. In addition, MSA is robust to imperfect clustering. It could also be combined with other means such as ECC, repeated markers, or any other code constraints. Furthermore, by selecting an appropriate sequencing depth, this strategy could achieve an optimal trade-off between cost and reading speed. MSA could be a competitive alternative for future DNA storage.