2024/01/28 by Anina Gruica, Gruica, Anina, Daniella Bar-Lev +5 · 3 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · #Advanced biosensing and bioanalysis techniques #Algorithms and Data Compression #Combinatorics (math.CO) #DNA and Biological Computing #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2401.15722
openalex publication_date 2024/01/28 · openalex created_date 2024/01/31 · openalex updated_date 2026/07/28
We investigate the fundamental limits of the recently proposed random access coverage depth problem for DNA data storage. Under this paradigm, it is assumed that the user information consists of k information strands, which are encoded into n strands via a generator matrix G. During the sequencing process, the strands are read uniformly at random, as each strand is available in a large number of copies. In this context, the random access coverage depth problem refers to the expected number of reads (i.e., sequenced strands) required to decode a specific information strand requested by the user. This problem heavily depends on the generator matrix G, and besides computing the expectation for different choices of G, the goal is to construct matrices that minimize the maximum expectation over all possible requested information strands, denoted by Tmax(G). In this paper, we introduce new techniques to investigate the random access coverage depth problem, capturing its combinatorial nature and identifying the structural properties of generator matrices that are advantageous. We establish two general formulas to determine Tmax(G) for arbitrary generator matrices. The first formula depends on the linear dependencies between columns of G, whereas the second formula takes into account recovery sets and their intersection structure. We also introduce the concept of recovery balanced codes and provide three sufficient conditions for a code to be recovery balanced. These conditions can be used to compute Tmax(G) for various families of codes, such as MDS, simplex, Hamming, and binary Reed-Muller codes. Additionally, we study the performance of modified systematic MDS and simplex matrices, showing that the best results for Tmax(G) are achieved with a specific combination of encoded strands and replication of the information strands.