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arXiv · 2511.14284

DNA Storage in the Short Molecule Regime

Ran Tamir·Nir Weinberger·Albert Guillén i Fàbregas
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Abstract

We study the amount of reliable information that can be stored in a DNA-based storage system composed of short DNA molecules. In this regime, Shomorony and Heckel (2022) put forward a conjecture on the scaling of the number of information bits that can be reliably stored. In this paper, we complete the proof of this conjecture. We analyze a random-coding scheme in which each codeword is obtained by quantizing a randomly generated probability mass function drawn from the probability simplex. By analyzing the optimal maximum-likelihood decoder, we derive an achievability bound that matches a recently established converse bound across the entire short-molecule regime. We also propose a second coding scheme, which operates with significantly lower computational complexity but achieves the optimal scaling, except for a specific range of very short molecules.

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Ran Tamir, Nir Weinberger, Albert Guillén i Fàbregas. 2025-11-18. DNA Storage in the Short Molecule Regime. https://arxiv.org/abs/2511.14284

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