On the Reliability of Information Retrieval from MDS Coded Data in DNA Storage

This work presents a theoretical analysis of the probability of successfully retrieving data encoded with MDS codes (e.g., Reed-Solomon codes) in DNA storage systems. We study this probability under independent and identically distributed (i.i.d.) substitution errors, focusing on a common code design strategy that combines inner and outer MDS codes. Our analysis demonstrates how this probability depends on factors such as the total number of sequencing reads, their distribution across strands, the rates of the inner and outer codes, and the substitution error probabilities. These results provide actionable insights into optimizing DNA storage systems under reliability constraints, including determining the minimum number of sequencing reads needed for reliable data retrieval and identifying the optimal balance between the rates of inner and outer MDS codes.