On Unique Error Patterns in the Levenshtein's Sequence Reconstruction Model

In the Levenshtein's sequence reconstruction problem a codeword is transmitted through N channels and in each channel a set of errors is introduced to the transmitted word. In previous works, the restriction that each channel provides a unique output word has been essential. In this work, we as...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 71; no. 7; pp. 5720 - 5736
Main Authors: Junnila, Ville, Laihonen, Tero, Lehtila, Tuomo
Format: Journal Article
Language:English
Published: IEEE 01.07.2025
Subjects:
Channel models
Codes
Decoding
decoding algorithm
deletion errors
DNA-memory
Information retrieval
insertion errors
Levenshtein’s sequence reconstruction
Mathematical models
Racetrack memory
Redundancy
substitution errors
Symbols
Terminology
Vectors
Zinc
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:In the Levenshtein's sequence reconstruction problem a codeword is transmitted through N channels and in each channel a set of errors is introduced to the transmitted word. In previous works, the restriction that each channel provides a unique output word has been essential. In this work, we assume only that each channel introduces a unique set of errors to the transmitted word and hence, some output words can also be identical. As we will discuss, this interpretation is both natural and useful for deletion and insertion errors. We give properties, techniques and (optimal) results for this situation. Quaternary alphabets are relevant due to applications related to DNA-memories. Hence, we introduce an efficient Las Vegas style decoding algorithm for simultaneous insertion, deletion and substitution errors in q -ary Hamming spaces for <inline-formula> <tex-math notation="LaTeX">q \geq 4 </tex-math></inline-formula>.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2025.3568068