Correcting a Single Deletion in Reads from a Nanopore Sequencer
Anisha Banerjee, Yonatan Yehezkeally, Antonia Wachter-Zeh, Eitan Yaakobi
TL;DR
This work analyzes deletion errors in a nanopore-inspired $\ell$-read channel for DNA storage, proving a fundamental redundancy lower bound of $\log n - \ell$ bits for correcting a single deletion and providing a near-optimal construction. It introduces a VT-like single-deletion $\ell$-read code with $\log_2(n+1)$ redundancy and shows how two independent noisy $\ell$-read vectors (for $\ell \\ge 2$) enable exact, zero-redundancy reconstruction without coding overhead. The approach combines a reduction to $\ell$-sticky deletions, a generalized sphere-packing bound, and a practical reconstruction algorithm, highlighting how nanopore-specific error structure can reduce storage-recovery costs. These results have practical implications for robust data retrieval in nanopore-based DNA storage systems and motivate further study of multi-read and multi-deletion scenarios.
Abstract
Owing to its several merits over other DNA sequencing technologies, nanopore sequencers hold an immense potential to revolutionize the efficiency of DNA storage systems. However, their higher error rates necessitate further research to devise practical and efficient coding schemes that would allow accurate retrieval of the data stored. Our work takes a step in this direction by adopting a simplified model of the nanopore sequencer inspired by Mao \emph{et al.}, which incorporates some of its physical aspects. This channel model can be viewed as a sliding window of length $\ell$ that passes over the incoming input sequence and produces the Hamming weight of the enclosed $\ell$ bits, while shifting by one position at each time step. The resulting $(\ell+1)$-ary vector, referred to as the $\ell$-\emph{read vector}, is susceptible to deletion errors due to imperfections inherent in the sequencing process. We establish that at least $\log n - \ell$ bits of redundancy are needed to correct a single deletion. An error-correcting code that is optimal up to an additive constant, is also proposed. Furthermore, we find that for $\ell \geq 2$, reconstruction from two distinct noisy $\ell$-read vectors can be accomplished without any redundancy, and provide a suitable reconstruction algorithm to this effect.