On the Maximum Number of Non-Confusable Strings Evolving under Short Tandem Duplications

The set of all -ary strings that do not contain repeated substrings of length (i.e., that do not contain substrings of the form , , and ) constitutes a code correcting an arbitrary number of tandem-duplication mutations of length . In other words, any two such strings are non-confusable in the sense...

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Bibliographic Details
Published in:Problems of information transmission 2022-04, Vol.58 (2), p.111-121
Main Author: Kovačević, M.
Format: Article
Language:English
Subjects:
639/301/1034/1035
639/925/357/995
Coding Theory
Communications Engineering
Control
Electrical Engineering
Engineering
Evolution
Information Storage and Retrieval
Mutation
Networks
Reproduction (copying)
Strings
Systems Theory
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Summary:The set of all -ary strings that do not contain repeated substrings of length (i.e., that do not contain substrings of the form , , and ) constitutes a code correcting an arbitrary number of tandem-duplication mutations of length . In other words, any two such strings are non-confusable in the sense that they cannot produce the same string while evolving under tandem duplications of length . We demonstrate that this code is asymptotically optimal in terms of rate, meaning that it represents the largest set of non-confusable strings up to subexponential factors. This result settles the zero-error capacity problem for the last remaining case of tandem-duplication channels satisfying the “root-uniqueness” property.
ISSN:0032-9460
1608-3253
DOI:10.1134/S0032946022020028