Approximate Trace Reconstruction: Algorithms

Sami Davies, Miklos Z. Racz, Benjamin G. Schiffer, Cyrus Rashtchian

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We introduce approximate trace reconstruction, a relaxed version of the trace reconstruction problem. Here, instead of learning a binary string perfectly from noisy samples, as in the original trace reconstruction problem, the goal is to output a string that is close in edit distance to the original string using few traces. We present several algorithms that can approximately reconstruct strings that belong to certain classes, where the estimate is within n / polylog (n) edit distance and where we only use polylog (n) traces (or sometimes just a single trace). These classes contain strings that require a linear number of traces for exact reconstruction and that are quite different from a typical random string. From a technical point of view, our algorithms approximately reconstruct consecutive substrings of the unknown string by aligning dense regions of traces and using a run of a suitable length to approximate each region. A full version of this paper is accessible at: https://arxiv.org/abs/2012.06713.pdf

Original languageEnglish (US)
Title of host publication2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2525-2530
Number of pages6
ISBN (Electronic)9781538682098
DOIs
StatePublished - Jul 12 2021
Event2021 IEEE International Symposium on Information Theory, ISIT 2021 - Virtual, Melbourne, Australia
Duration: Jul 12 2021Jul 20 2021

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2021-July
ISSN (Print)2157-8095

Conference

Conference2021 IEEE International Symposium on Information Theory, ISIT 2021
Country/TerritoryAustralia
CityVirtual, Melbourne
Period7/12/217/20/21

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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