On the Decoding Complexity of Cyclic Codes Up to the BCH Bound

Davide Schipani; Michele Elia; Joachim Rosenthal

doi:10.1109/isit.2011.6034253

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arXiv · 1102.2939

On the Decoding Complexity of Cyclic Codes Up to the BCH Bound

Davide Schipani·Michele Elia·Joachim Rosenthal

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Abstract

The standard algebraic decoding algorithm of cyclic codes $[n,k,d]$ up to the BCH bound $t$ 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 $O(t\sqrt n)$, and that of the error location from $O(nt)$ to at most $\max \{O(t\sqrt n), O(t^2\log(t)\log(n))\}$.

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Davide Schipani, Michele Elia, Joachim Rosenthal. 2011-05-27. On the Decoding Complexity of Cyclic Codes Up to the BCH Bound. https://doi.org/10.1109/isit.2011.6034253

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