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Published on: February 6, 2014
Three Efficient All-Erasure Decoding Methods for Blaum-Roth Codes
1School of Computer Science and Technology, Dongguan University of Technology, Dongguan 523820, China.
Abstract:
Blaum-Roth Codes are binary maximum distance separable (MDS) array codes over the binary quotient ring F2[x]/(Mp(x)), where Mp(x)=1+x+⋯+xp-1, and p is a prime number. Two existing all-erasure decoding methods for Blaum-Roth codes are the syndrome-based decoding method and the interpolation-based decoding method. In this paper, we propose a modified syndrome-based decoding method and a modified interpolation-based decoding method that have lower decoding complexity than the syndrome-based decoding method and the interpolation-based decoding method, respectively. Moreover, we present a fast decoding method for Blaum-Roth codes based on the LU decomposition of the Vandermonde matrix that has a lower decoding complexity than the two modified decoding methods for most of the parameters.
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