On Subsets of Binary Strings Immune to Multiple Repetition Errors
Dolecek, Lara
Anantharam, Venkat
EECS Department, University of California, Berkeley, CA 94720, USA. Email: dolecek@eecs.berkeley.edu;
This paper appears in: Information Theory, 2007. ISIT 2007. IEEE International Symposium on
Publication Date: 24-29 June 2007
On page(s): 1691-1695
Location: Nice,
ISBN: 978-1-4244-1397-3
Digital Object Identifier: 10.1109/ISIT.2007.4557465
Current Version Published: 2008-07-09
Abstract
In this paper we revisit previously proposed techniques for constructing some families of subsets of binary strings (codes) that are immune to multiple repetition errors. In particular, we discuss a technique to construct single repetition error correcting codes and use number theoretic methods to give an explicit formula for the cardinalities of these codes. This approach results in codes the ratio of whose cardinality to the best upper bounds approaches unity in the increasing codelength limit (asymptotic optimality). We also discuss a somewhat different technique to construct multiple repetition error correcting codes. Here the cardinalities are asymptotically within a fixed constant of the best known upper bounds. Our constructions are asymptotically better by a constant factor than the best previously known such constructions, due to Levenshtein.
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