Separating erasures from errors for decoding
Abdel-Ghaffar, K.A.
Weber, J.H.
Dept. ECE, Univ. of California, Davis, CA;
This paper appears in: Information Theory, 2008. ISIT 2008. IEEE International Symposium on
Publication Date: 6-11 July 2008
On page(s): 215-219
Location: Toronto, ON,
ISBN: 978-1-4244-2256-2
INSPEC Accession Number: 10156263
Digital Object Identifier: 10.1109/ISIT.2008.4594979
Current Version Published: 2008-08-08
Abstract
Most decoding algorithms of linear codes, in general, are designed to correct or detect errors. However, many channels cause erasures in addition to errors. In principle, decoding over such channels can be accomplished by deleting the erased symbols and decoding the resulting vector with respect to a punctured code. For any given linear code and any given maximum number of correctable erasures, we introduce parity-check matrices yielding parity-check equations that do not check any of the erased symbols and which are sufficient to characterize all punctured codes corresponding to this maximum number of erasures. This allows for the separation of erasures from errors to facilitate decoding. The parity-check matrices typically have redundant rows. We give several constructions of such matrices and prove general bounds on their minimum sizes.
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