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An Improved Bound on the Fraction of Correctable Deletions
KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.ORCID iD: 0000-0002-5379-345X
2017 (English)In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 63, no 1, p. 93-103Article in journal (Refereed) Published
Abstract [en]

We consider codes over fixed alphabets against worst case symbol deletions. For any fixed k >= 2, we construct a family of codes over alphabet of size k with positive rate, which allow efficient recovery from a worst case deletion fraction approaching 1 - (2/(k + root k)). In particular, for binary codes, we are able to recover a fraction of deletions approaching 1/(root 2+1) = root 2-1 approximate to 0.414. Previously, even non-constructively, the largest deletion fraction known to be correctable with positive rate was 1 - Theta (1/root k), and around 0.17 for the binary case. Our result pins down the largest fraction of correctable deletions for k-ary codes as 1 - Theta (1/k), since 1 - 1/k is an upper bound even for the simpler model of erasures where the locations of the missing symbols are known. Closing the gap between (root 2 - 1) and 1/2 for the limit of worst case deletions correctable by binary codes remains a tantalizing open question.

Place, publisher, year, edition, pages
IEEE, 2017. Vol. 63, no 1, p. 93-103
Keywords [en]
Error-correction, deletion codes, combinatorics, concatenated coding
National Category
Computer and Information Sciences
Identifiers
URN: urn:nbn:se:kth:diva-201242DOI: 10.1109/TIT.2016.2621044ISI: 000391740000007Scopus ID: 2-s2.0-85008473100OAI: oai:DiVA.org:kth-201242DiVA, id: diva2:1074827
Conference
ACM-SIAM Symposium on Discrete Algorithms, JAN 10-12, 2016, Arlington, VA
Note

QC 20170216

Available from: 2017-02-16 Created: 2017-02-16 Last updated: 2018-01-13Bibliographically approved

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Håstad, Johan

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