DNA Storage in the Short Molecule Regime

TL;DR

This paper proves a conjecture about the maximum reliable information storage in short DNA molecules, matching theoretical bounds and proposing efficient coding schemes for DNA data storage.

Contribution

It completes the proof of a conjecture on DNA storage capacity in the short molecule regime and introduces coding schemes that achieve optimal scaling.

Findings

Achieves an achievability bound matching the converse bound.

Proposes a low-complexity coding scheme with near-optimal scaling.

Provides theoretical validation for DNA storage capacity limits.

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.