DNA Tails for Molecular Flash Memory

TL;DR

This work introduces DNA Tails, a nonbinary DNA data-storage paradigm that encodes information at nicking sites by growing variable-length single-stranded tails and interpreting their average lengths via rank modulation. By using staggered nicking-tail extension, the method translates tail-length information into a larger alphabet, increasing storage density beyond prior one-bit-per-site approaches while mitigating calibration errors through rank modulation. The authors identify tails that stop growing (stumped tails) as a primary error source and develop three complementary rank-modulation–based code families to correct stuck-at errors: (i) Lehmer-encoded permutations with Reed-Solomon erasure coding for the $t$-stuck-at model, (ii) burst-stuck-at codes that partition symbol values into blocks and interleave redundancies to guard against bursts, and (iii) rank-modulation codes that use parity checks on the inverse permutation to correct rank-based stuck-at errors. Together with encoding/decoding algorithms and order-optimal redundancy demonstrations, the work provides a practical theoretical framework and experimental validation for robust, high-density DNA-based storage using topological tail encoding.

Abstract

DNA-based data storage systems face practical challenges due to the high cost of DNA synthesis. A strategy to address the problem entails encoding data via topological modifications of the DNA sugar-phosphate backbone. The DNA Punchcards system, which introduces nicks (cuts) in the DNA backbone, encodes only one bit per nicking site, limiting density. We propose \emph{DNA Tails,} a storage paradigm that encodes nonbinary symbols at nicking sites by growing enzymatically synthesized single-stranded DNA of varied lengths. The average tail lengths encode multiple information bits and are controlled via a staggered nicking-tail extension process. We demonstrate the feasibility of this encoding approach experimentally and identify common sources of errors, such as calibration errors and stumped tail growth errors. To mitigate calibration errors, we use rank modulation proposed for flash memory. To correct stumped tail growth errors, we introduce a new family of rank modulation codes that can correct ``stuck-at'' errors. Our analytical results include constructions for order-optimal-redundancy permutation codes and accompanying encoding and decoding algorithms.

Figures (2)

• Figure 1: An overview of our DNA Tail framework. (a) Schematic of Tail-length encoding, showing the locations were tails can be grown according to the natural order on the DNA backbone. (b) Schematic of the general multi-round, nonbinary approach for recording information in DNA tails (i.e., single-stranded DNA fragments enzymatically synthesized on double-stranded substrates). For low-cost, we use native restriction endonucleases for nicking and the TdT polymerase for tail growths. (c,d) Schematics of rank modulation for tail and cell "charges."
• Figure 2: (a) Schematic of the image encoding procedure, explained in the main text. (b) Results of recording a signature DNA tail $20$ on the first synthetic DNA image. (c) Matching results for gBlocks encoding the right image in (a), with the superimposed value $5030$. (d) Rank modulation experiments on the encoding of the poem A Dream Within a Dream by E. A. Poe using three gBlocks. (e) Rank modulation errors.

Theorems & Definitions (26)

• Example 1
• Example 2
• Example 3
• Theorem 1
• Remark 1
• Lemma 1
• proof
• Lemma 2
• proof
• Theorem 2