A1 Refereed original research article in a scientific journal
On t-revealing codes in binary Hamming spaces
Authors: Laihonen Tero
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Publication year: 2019
Journal: Information and Computation
Journal acronym: INFORM COMPUT
Article number: UNSP 104455
Volume: 268
Number of pages: 11
ISSN: 0890-5401
eISSN: 1090-2651
DOI: https://doi.org/10.1016/j.ic.2019.104455
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/42496316
Abstract
In this paper, we introduce t-revealing codes in the binary Hamming space F-n. Let C subset of F-n be a code and denote by I-t (C; x) the set of elements of C which are within (Hamming) distance t from a word x is an element of F-n. A code C is t-revealing if the majority voting on the coordinates of the words in I-t (C; x) gives unambiguously x. These codes have applications, for instance, to the list decoding problem of the Levenshtein's channel model, where the decoder provides a list based on several different outputs of the channel with the same input, and to the information retrieval problem of the Yaakobi-Bruck model of associative memories. We give t-revealing codes which improve some of the key parameters for these applications compared to earlier code constructions. (C) 2019 Elsevier Inc. All rights reserved.
In this paper, we introduce t-revealing codes in the binary Hamming space F-n. Let C subset of F-n be a code and denote by I-t (C; x) the set of elements of C which are within (Hamming) distance t from a word x is an element of F-n. A code C is t-revealing if the majority voting on the coordinates of the words in I-t (C; x) gives unambiguously x. These codes have applications, for instance, to the list decoding problem of the Levenshtein's channel model, where the decoder provides a list based on several different outputs of the channel with the same input, and to the information retrieval problem of the Yaakobi-Bruck model of associative memories. We give t-revealing codes which improve some of the key parameters for these applications compared to earlier code constructions. (C) 2019 Elsevier Inc. All rights reserved.
Keywords:
Levenshtein's sequence reconstruction problem, List decoding, Majority voting on coordinates
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