2021
DOI: 10.48550/arxiv.2111.14026
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Bounds and Constructions for Insertion and Deletion Codes

Abstract: Insertion and deletion (insdel for short) codes have recently attracted a lot of attention due to their applications in many interesting fields such as DNA storage, DNA analysis, race-track memory error correction and language processing. The present paper mainly studies limits and constructions of insdel codes. The paper can be divided into two parts. The first part focuses on various bounds, while the second part concentrates on constructions of insdel codes.Although the insdel-metric Singleton bound has bee… Show more

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Cited by 1 publication
(2 citation statements)
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References 19 publications
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“…Here, ρ (δ,L) (1 − τ D ) is a piecewise linear function with L linear pieces where it coincides with the unique decoding bound τ I < δ − τ D when τ D 1 − L+1 L−1 (1 − δ). Such result provides a lower bound on the insdellist-decodability of a code given the values of δ, τ I , τ D and L. As illustrated in Section VI, Theorem IV.1 provides an insdel-list-decodability results for various constructions of codes, including some Reed-Solomon codes [31], [32], [33], [34], [35], Varshamov-Tenengolts (VT for short) codes [14], [15], [17] and Helberg codes [36], [37]. This provides such constructions with a stronger property on their insdel-list-decodability, as can be observed in Theorems VI.1, VI.2 and VI.3 respectively.…”
Section: Our Main Contributionmentioning
confidence: 91%
See 1 more Smart Citation
“…Here, ρ (δ,L) (1 − τ D ) is a piecewise linear function with L linear pieces where it coincides with the unique decoding bound τ I < δ − τ D when τ D 1 − L+1 L−1 (1 − δ). Such result provides a lower bound on the insdellist-decodability of a code given the values of δ, τ I , τ D and L. As illustrated in Section VI, Theorem IV.1 provides an insdel-list-decodability results for various constructions of codes, including some Reed-Solomon codes [31], [32], [33], [34], [35], Varshamov-Tenengolts (VT for short) codes [14], [15], [17] and Helberg codes [36], [37]. This provides such constructions with a stronger property on their insdel-list-decodability, as can be observed in Theorems VI.1, VI.2 and VI.3 respectively.…”
Section: Our Main Contributionmentioning
confidence: 91%
“…This implies that for such choice of the evaluation points, the minimum Levenshtein distance is at least 2n − 4k + 4. Although there have been numerous works on the insdel-correcting capabilities of Reed-Solomon codes (see, for example [31], [32], [33], [34], [35]), there have not been any study on its list-decoding capability. It is easy to see from Theorem IV.1 that the upper bound for t I increases as the minimum Levenshtein distance increases.…”
Section: A Reed-solomon Codesmentioning
confidence: 99%