Self-checking circuits and decoding algorithms for binary hamming and BCH codes and Reed-Solomon codes over GF(2 m )

Self-checking circuits and decoding algorithms for binary hamming and BCH codes and Reed-Solomon... We consider problems of detecting errors in combinational circuits and algorithms for the decoding of linear codes. We show that a totally self-checking combinatorial circuit for the decoding of a binary Hamming [n, k] code can be constructed if and only if n = 2 r − 1, r = n−k. We introduce the notion of a totally self-checking combinational circuit detecting error clusters of size at most µ; for shortened Hamming [n,k] codes, we construct totally self-checking decoding combinational circuits detecting error clusters of size at most µ, 2 ≤ µ < n−k. We describe single-error protected and self-checking algorithms: the extended Euclidean algorithm and decoding algorithms for binary BCH codes and Reed-Solomon codes over GF(2 m ). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

Self-checking circuits and decoding algorithms for binary hamming and BCH codes and Reed-Solomon codes over GF(2 m )

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Publisher
SP MAIK Nauka/Interperiodica
Copyright
Copyright © 2008 by Pleiades Publishing, Ltd.
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946008020038
Publisher site
See Article on Publisher Site

Abstract

We consider problems of detecting errors in combinational circuits and algorithms for the decoding of linear codes. We show that a totally self-checking combinatorial circuit for the decoding of a binary Hamming [n, k] code can be constructed if and only if n = 2 r − 1, r = n−k. We introduce the notion of a totally self-checking combinational circuit detecting error clusters of size at most µ; for shortened Hamming [n,k] codes, we construct totally self-checking decoding combinational circuits detecting error clusters of size at most µ, 2 ≤ µ < n−k. We describe single-error protected and self-checking algorithms: the extended Euclidean algorithm and decoding algorithms for binary BCH codes and Reed-Solomon codes over GF(2 m ).

Journal

Problems of Information TransmissionSpringer Journals

Published: Jul 11, 2008

References

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