On the List Decodability of Insertions and Deletions
Tomohiro Hayashi, Kenji Yasunaga

TL;DR
This paper establishes bounds and algorithms for list decoding of codes affected by insertions and deletions, showing that certain codes can reliably correct high fractions of such errors.
Contribution
It introduces a Johnson-type upper bound for list decoding with insertions and deletions, and provides efficient encoding and decoding algorithms for these error types.
Findings
Binary codes can be list-decoded from 0.707 fraction of insertions.
Existence of q-ary codes with high rate decodable from specified insertion and deletion fractions.
Derived a Plotkin-type upper bound on code size in the Levenshtein metric.
Abstract
In this work, we study the problem of list decoding of insertions and deletions. We present a Johnson-type upper bound on the maximum list size. The bound is meaningful only when insertions occur. Our bound implies that there are binary codes of rate that are list-decodable from a -fraction of insertions. For any and , there exist -ary codes of rate that are list-decodable from a -fraction of insertions and -fraction of deletions, where depends only on and . We also provide efficient encoding and decoding algorithms for list-decoding from -fraction of insertions and -fraction of deletions for any and . Based on the Johnson-type bound, we derive a…
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Taxonomy
TopicsDNA and Biological Computing · Coding theory and cryptography · Advanced biosensing and bioanalysis techniques
