Explicit and Efficient Constructions of Linear Codes Against Adversarial Insertions and Deletions

Roni Con*, Amir Shpilka, Itzhak Tamo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this work, we study linear error-correcting codes against adversarial insertion-deletion (insdel) errors, a topic that has recently gained a lot of attention. We construct linear codes over Fq, for q= poly(1/ϵ), that can efficiently decode from a δ fraction of insdel errors and have rate (1-4\delta)/8-ϵ. We also show that by allowing codes over Fq2 that are linear over Fq, we can improve the rate to (1-δ)/4-ϵ while not sacrificing efficiency. Using this latter result, we construct fully linear codes over F2 that can efficiently correct up to δ < 1/54 fraction of deletions and have rate R = (1-54⊙δ)/1216. Cheng et al. (2021) constructed codes with (extremely small) rates bounded away from zero that can correct up to a δ < 1/400 fraction of insdel errors. They also posed the problem of constructing linear codes that get close to the half-Singleton bound [proved in Cheng et al. (2021)] over small fields. Thus, our results significantly improve their construction and get much closer to the bound.

Original languageEnglish
Pages (from-to)6516-6526
Number of pages11
JournalIEEE Transactions on Information Theory
Volume68
Issue number10
DOIs
StatePublished - 1 Oct 2022

Funding

FundersFunder number
Horizon 2020 Framework Programme852953

    Keywords

    • Insertion-deletion codes
    • linear insdel codes

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