# Image Storage in DNA by an Extensible Quaternary Codec System
## 3 Results  
The performance of the ETQ was validated through in vitro experiments and in silicon experiments, and all images were successfully restored (the results are shown in Figure 5). In the in vitro experiments, we synthesized 1,037,400 bits of image data (image ID: 0). The synthetic DNA sequences were stored at room temperature for three days and subsequently frozen for another three days. After sequencing, the image was successfully recovered. Due to the limitations of DNA synthesis technology (short DNA strands have the highest synthesis efficiency [22; 23; 24; 33]), the synthesized sequences were all 150 nt in length, resulting in a total of 4891 DNA sequences (733,650 nt). These DNA sequences exhibited a GC content of approximately 50%, homopolymer lengths shorter than 4 nt, and a net information density of about 1.41 bits/nt (as shown in Figure 6). In the computer simulation experiments, in addition to image ID 0, we tested three other images. For each image, the DNA strand length used for storage was varied among 150 nt, 200 nt, 250 nt, 300 nt, 350 nt, and 400 nt. Figure 6a shows the relationship between the net information density and DNA strand length for different images. Taking image ID 0 as an example, the GC content and homopolymer length of sequences with different lengths were controlled to match the in vitro experiments. However, due to the increased length of the data segments,  
Figure 4: Flow diagram of RS error correction and decoding algorithm.  
the net information density for sequences of 150 nt, 200 nt, 250 nt, 300 nt, 350 nt, and 400 nt was 1.71 bits/nt, 1.94 bits/nt, 2.07 bits/nt, 2.14 bits/nt, and 2.22 bits/nt, respectively. This broke the storage density limit of 2 bits/nt previously achieved by other encoding systems (Figure 1).  
Additionally, all the curves in Figure 6a show a trend of increasing net information density with increasing DNA strand length, but the rate of increase gradually diminishes, indicating a trend toward saturation. The curve for image ID \"0.jpg\" is consistently higher than the others, suggesting that its net information density is the highest under given conditions. Overall, there is a positive correlation between DNA strand length and net information density, although the specific form of this relationship varies significantly depending on the image content. Short DNA strands may be limited by boundary effects and a constrained information space, resulting in lower information density. In contrast, longer DNA strands exhibit greater redundancy tolerance, allowing for more efficient information storage. This finding provides important insights into the optimization of DNA storage and encoding strategies, highlighting the critical role of DNA strand length and encoding methods in the design of high-density DNA molecules. At this stage, there are various encoding systems in the field, making it difficult to test different DNA data storage systems on the same dataset. Therefore, we followed the conventions in the DNA digital storage field [10; 14] by testing system performance on their respective datasets. Through comparisons and predictions of net information density, despite the ETQ's net information density in in vitro experiments not exceeding 2 bits/nt, it remains the most feasible and extensible DNA storage system published in recent years.  
Figure 5: A successful reconstruction, which demonstrates the successful decoding and image reconstruction process from DNA-based storage and validates the feasibility of DNA-based image storage and retrieval via the ETQ.  
Figure 6: (**a**) The relationship between the length of the DNA strands (in nucleotides) and their net information density (in bits per nucleotide); (**b**) the composition of CG distribution in the encoded DNA sequence.