Publication: On the decoding complexity of cyclic codes up to the BCH bound
On the decoding complexity of cyclic codes up to the BCH bound
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Schipani, D., Elia, M., & Rosenthal, J. (2011). On the decoding complexity of cyclic codes up to the BCH bound. In IEEE (Ed.), IEEE International Symposium on Information Theory proceedings (ISIT), 2011 : July 31, 2011 - Aug. 5, 2011, St. Petersburg, Russia (pp. 835–839). IEEE. https://doi.org/10.1109/ISIT.2011.6034253
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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
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- Schipani, D
- Elia, M
- Rosenthal, J
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Schipani, D., Elia, M., & Rosenthal, J. (2011). On the decoding complexity of cyclic codes up to the BCH bound. In IEEE (Ed.), IEEE International Symposium on Information Theory proceedings (ISIT), 2011 : July 31, 2011 - Aug. 5, 2011, St. Petersburg, Russia (pp. 835–839). IEEE. https://doi.org/10.1109/ISIT.2011.6034253