# Coded Trace Reconstruction

Mahdi Cheraghchi, Ryan Gabrys, Olgica Milenkovic, Joao Ribeiro

Research output: Contribution to journalArticlepeer-review

## Abstract

Motivated by average-case trace reconstruction and coding for portable DNA-based storage systems, we initiate the study of coded trace reconstruction, the design and analysis of high-rate efficiently encodable codes that can be efficiently decoded with high probability from few reads (also called traces) corrupted by edit errors. Codes used in current portable DNA-based storage systems with nanopore sequencers are largely based on heuristics, and have no provable robustness or performance guarantees even for an error model with i.i.d. deletions and constant deletion probability. Our work is the first step towards the design of efficient codes with provable guarantees for such systems. We consider a constant rate of i.i.d. deletions, and perform an analysis of marker-based code-constructions. This gives rise to codes with redundancy $O(n/\log n)$ (resp. $O(n/\log \log n)$ ) that can be efficiently reconstructed from $\exp (O(\log ^{2/3}n))$ (resp. $\exp (O(\log \log n)^{2/3})$ ) traces, where $n$ is the message length. Then, we give a construction of a code with $O(\log n)$ bits of redundancy that can be efficiently reconstructed from $\text {poly}(n)$ traces if the deletion probability is small enough. Finally, we show how to combine both approaches, giving rise to an efficient code with $O(n/\log n)$ bits of redundancy which can be reconstructed from $\text {poly}(\log n)$ traces for a small constant deletion probability.

Original language English (US) 9097932 6084-6103 20 IEEE Transactions on Information Theory 66 10 https://doi.org/10.1109/TIT.2020.2996377 Published - Oct 2020

## Keywords

• Coding
• DNA storage
• deletion channel
• trace reconstruction

## ASJC Scopus subject areas

• Information Systems
• Computer Science Applications
• Library and Information Sciences