REPETITION ERROR CORRECTING SETS: EXPLICIT CONSTRUCTIONS AND PREFIXING METHODS
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Dolecek-2010-REPETITION ERROR COR.pdf
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Author(s)
Dolecek, Lara
Anantharam, Venkat
Date Issued
January 2010
Journal
SIAM Journal on Discrete Mathematics
Publisher
Society for Industrial and Applied Mathematics.
Citation
Dolecek, Lara, and Venkat Anantharam. “Repetition Error Correcting Sets: Explicit Constructions and Prefixing Methods.” SIAM Journal on Discrete Mathematics 23.4 (2010) : 2120. © 2010 Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
In this paper we study the problem of finding maximally sized subsets of binary
strings (codes) of equal length that are immune to a given number r of repetitions, in the sense that no
two strings in the code can give rise to the same string after r repetitions. We propose explicit number
theoretic constructions of such subsets. In the case of r = 1 repetition, the proposed construction
is asymptotically optimal. For r ≥ 1, the proposed construction is within a constant factor of the
best known upper bound on the cardinality of a set of strings immune to r repetitions. Inspired
by these constructions, we then develop a prefixing method for correcting any prescribed number r
of repetition errors in an arbitrary binary linear block code. The proposed method constructs for
each string in the given code a carefully chosen prefix such that the resulting strings are all of the
same length and such that despite up to any r repetitions in the concatenation of the prefix and the
codeword, the original codeword can be recovered. In this construction, the prefix length is made
to scale logarithmically with the length of strings in the original code. As a result, the guaranteed
immunity to repetition errors is achieved while the added redundancy is asymptotically negligible.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
https://doi.org/10.1137/080730093
