The Geometry of Codes for Random Access in DNA Storage

TL;DR

This paper introduces a geometric approach to DNA storage codes, improving random access efficiency by constructing better codes and proving a conjecture for rate 1/2 codes across dimensions.

Contribution

It presents a novel geometric framework for designing DNA storage codes, including a new construction for k=3 and a proof of a conjecture for rate 1/2 codes.

Findings

A new code construction for k=3 that reduces random access expectation.

Proof of a conjecture for rate 1/2 codes in any dimension.

Demonstrated improved performance over previous code constructions.

Abstract

Effective and reliable data retrieval is critical for the feasibility of DNA storage, and the development of random access efficiency plays a key role in its practicality and reliability. In this paper, we study the Random Access Problem, which asks to compute the expected number of samples one needs in order to recover an information strand. Unlike previous work, we took a geometric approach to the problem, aiming to understand which geometric structures lead to codes that perform well in terms of reducing the random access expectation (Balanced Quasi-Arcs). As a consequence, two main results are obtained. The first is a construction for $k=3$ that outperforms previous constructions aiming to reduce the random access expectation. The second, exploiting a result from~\cite{gruica2024reducing}, is the proof of a conjecture from~\cite{bar2023cover} for rate $1/2$ codes in any dimension.