Error-Correcting Codes for Combinatorial Composite DNA

TL;DR

This paper introduces error-correcting codes tailored for combinatorial composite DNA data storage, addressing unique asymmetric errors from shortmer-based synthesis, with theoretical bounds, explicit encoding/decoding, and experimental validation.

Contribution

It proposes novel error-correcting code constructions for composite DNA synthesis errors, including bounds, explicit algorithms, and experimental analysis.

Findings

Error-correcting codes effectively handle asymmetric shortmer errors.

Lower bounds on redundancy for these codes are established.

Experimental data supports the proposed error model and analysis.

Abstract

Data storage in DNA is developing as a possible solution for archival digital data. Recently, to further increase the potential capacity of DNA-based data storage systems, the combinatorial composite DNA synthesis method was suggested. This approach extends the DNA alphabet by harnessing short DNA fragment reagents, known as shortmers. The shortmers are building blocks of the alphabet symbols, consisting of a fixed number of shortmers. Thus, when information is read, it is possible that one of the shortmers that forms part of the composition of a symbol is missing and therefore the symbol cannot be determined. In this paper, we model this type of error as a type of asymmetric error and propose code constructions that can correct such errors in this setup. We also provide a lower bound on the redundancy of such error-correcting codes and give an explicit encoder and decoder pair for our construction. Our suggested error model is also supported by an analysis of data from actual experiments that produced DNA according to the combinatorial scheme. Lastly, we also provide a statistical evaluation of the probability of observing such error events, as a function of read depth.