Insertion and Deletion Correction in Polymer-based Data Storage

TL;DR

This paper explores error correction in polymer-based data storage, focusing on insertion and deletion errors in composition multisets, and proposes new coding constraints to improve robustness.

Contribution

It generalizes existing error models by including insertions and deletions, and develops new coding constraints for improved error correction in polymer storage.

Findings

Analysis of the robustness of existing reconstruction codebooks to insertion and deletion errors.

Proposal of new coding constraints to correct insertion and deletion errors in composition multisets.

Enhanced understanding of error models in polymer-based data storage systems.

Abstract

Synthetic polymer-based storage seems to be a particularly promising candidate that could help to cope with the ever-increasing demand for archival storage requirements. It involves designing molecules of distinct masses to represent the respective bits $\{0,1\}$, followed by the synthesis of a polymer of molecular units that reflects the order of bits in the information string. Reading out the stored data requires the use of a tandem mass spectrometer, that fragments the polymer into shorter substrings and provides their corresponding masses, from which the \emph{composition}, i.e. the number of $1$s and $0$s in the concerned substring can be inferred. Prior works have dealt with the problem of unique string reconstruction from the set of all possible compositions, called \emph{composition multiset}. This was accomplished either by determining which string lengths always allow unique reconstruction, or by formulating coding constraints to facilitate the same for all string lengths. Additionally, error-correcting schemes to deal with substitution errors caused by imprecise fragmentation during the readout process, have also been suggested. This work builds on this research by generalizing previously considered error models, mainly confined to substitution of compositions. To this end, we define new error models that consider insertions of spurious compositions and deletions of existing ones, thereby corrupting the composition multiset. We analyze if the reconstruction codebook proposed by Pattabiraman \emph{et al.} is indeed robust to such errors, and if not, propose new coding constraints to remedy this.