DNA Tails for Molecular Flash Memory

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.