Coding for Synthesis Defects

TL;DR

This paper introduces novel coding schemes to correct synthesis defects in DNA data storage, focusing on defective cycles during parallel DNA synthesis and providing constructions with near-optimal redundancy.

Contribution

It proposes two families of codes for correcting synthesis defects, with explicit constructions and redundancy bounds, advancing error correction in DNA-based data storage systems.

Findings

Constructed codes for t=1,2 with specific redundancies

Provided a lower bound on redundancy for single-known defects

Demonstrated near-optimality of the proposed codes

Abstract

Motivated by DNA based data storage system, we investigate the errors that occur when synthesizing DNA strands in parallel, where each strand is appended one nucleotide at a time by the machine according to a template supersequence. If there is a cycle such that the machine fails, then the strands meant to be appended at this cycle will not be appended, and we refer to this as a synthesis defect. In this paper, we present two families of codes correcting synthesis defects, which are t-known-synthesis-defect correcting codes and t-synthesis-defect correcting codes. For the first one, it is assumed that the defective cycles are known, and each of the codeword is a quaternary sequence. We provide constructions for this family of codes for t = 1, 2, with redundancy log 4 and log n+18 log 3, respectively. For the second one, the codeword is a set of M ordered sequences, and we give constructions for t = 1, 2 to show a strategy for constructing this family of codes. Finally, we derive a lower bound on the redundancy for single-known-synthesis-defect correcting codes, which assures that our construction is almost optimal.