Sequence Reconstruction for Limited-Magnitude Errors

TL;DR

This paper investigates reconstruction and list-reconstruction methods for integer vectors affected by limited-magnitude errors, with applications to DNA storage, providing asymptotic analysis, efficient algorithms, and exploring code properties.

Contribution

It introduces new asymptotic bounds, efficient reconstruction algorithms, and extends these to list-reconstruction, including analysis of linear codes and connections to tandem-duplication channels.

Findings

Characterized the asymptotic size of error ball intersections.

Developed efficient algorithms for various error parameters.

Established trade-offs between list size and channel outputs.

Abstract

Motivated by applications to DNA storage, we study reconstruction and list-reconstruction schemes for integer vectors that suffer from limited-magnitude errors. We characterize the asymptotic size of the intersection of error balls in relation to the code's minimum distance. We also devise efficient reconstruction algorithms for various limited-magnitude error parameter ranges. We then extend these algorithms to the list-reconstruction scheme, and show the trade-off between the asymptotic list size and the number of required channel outputs. These results apply to all codes, without any assumptions on the code structure. Finally, we also study linear reconstruction codes with small intersection, as well as show a connection to list-reconstruction codes for the tandem-duplication channel.