The Coverage Depth Problem in DNA Storage Over Small Alphabets

TL;DR

This paper studies the coverage depth problem in DNA storage over small alphabets, deriving formulas and bounds for code performance when MDS codes are not available.

Contribution

It provides the first analysis of coverage depth for codes over small fields, including closed-form formulas and comparisons with theoretical bounds.

Findings

Derived closed-form formulas for expected reads

Compared code performance with theoretical bounds

Analyzed coverage depth for various code families

Abstract

The coverage depth problem in DNA data storage is about minimizing the expected number of reads until all data is recovered. When they exist, MDS codes offer the best performance in this context. This paper focuses on the scenario where the base field is not large enough to allow the existence of MDS codes. We investigate the performance for the coverage depth problem of codes defined over a small finite field, providing closed formulas for the expected number of reads for various code families. We also compare the results with the theoretical bounds in asymptotic regimes. The techniques we apply range from probability, to duality theory and combinatorics.