Family of Mutually Uncorrelated Codes for DNA Storage Address Design

Deoxyribonucleic acid (DNA) has become an ideal medium for long-term storage and retrieval due to its extremely high storage density and long-term stability. But access efficiency is an existing bottleneck in DNA storage, especially the lack of high-quality random access address sequences. Therefore, in this paper, we report a series of approaches based on k-weakly mutually uncorrelated (k-WMU) codes to design the address sequence to improve the access efficiency of DNA storage. To address the problem of DNA sequences that are poorly scalable at the base level, we propose a 0-m-ruling coding scheme combined with k-WMU codes that can make address sequences avoid generating secondary structure with stem lengths ranging from 3 to 9. Based on the decoupled structure, We further extend the k-WMU codes with error correction function while satisfying combinatorial biological constraints. In order to investigate the performance of the designed address sequences for real-world applications, we perform simulation experiments based on thermodynamic properties and error correction capability as well as compared the minimum free energy (MFE), melting temperature (TM), and average decoding success rate (ADSR) with previous work. The results show that designed address sequences have a high MFE value and ADSR and a substantial reduction in TM-variance while satisfying the combinatorial biological constraints. As the quality of address sequences improves, this will help to achieve accurate random access as well as enhance the robustness of the DNA storage system.