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<p>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 take 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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(k=3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>=</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation> that outperforms previous constructions aiming to reduce the random access expectation. The second, exploiting a result from Gruica et al. (Preprint, arXiv:2401.15722, 2024), is the proof of a conjecture from&#xa0;Bar-Lev et al. (Preprint, arXiv:2305.05656, 2023) for rate 1/2 codes in any dimension.</p>

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The geometry of codes for random access in DNA storage

  • 期刊论文

  • 发表日期：

    2026年5月16日

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  • Anina Gruica,
  • Maria Montanucci,
  • Ferdinando Zullo

摘要

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 take 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 \(k=3\) k = 3 that outperforms previous constructions aiming to reduce the random access expectation. The second, exploiting a result from Gruica et al. (Preprint, arXiv:2401.15722, 2024), is the proof of a conjecture from Bar-Lev et al. (Preprint, arXiv:2305.05656, 2023) for rate 1/2 codes in any dimension.