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On the decoding complexity of cyclic codes up to the BCH bound

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3 Author(s)
Schipani, D. ; Math. Inst., Univ. of Zurich, Zürich, Switzerland ; Elia, M. ; Rosenthal, J.

The standard algebraic decoding algorithm of cyclic codes [n, k, d] up to the BCH bound δ = 2t + 1 is very efficient and practical for relatively small n while it becomes unpractical for large n as its computational complexity is O(nt). Aim of this paper is to show how to make this algebraic decoding computationally more efficient: in the case of binary codes, for example, the complexity of the syndrome computation drops from O(nt) to O(t√n), while the average complexity of the error location drops from O(nt) to max{O(t√n), O(t log2(t)log log(t)log(n))}.

Published in:

Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on

Date of Conference:

July 31 2011-Aug. 5 2011