A New Approach to the Berlekamp-Massey-Sakata Algorithm: Improving Locator Decoding

We study the problem of the computation of Groebner basis for the ideal of linear recurring relations of a doubly periodic array. We find a set of indexes such that, along with some conditions, guarantees that the set of polynomials obtained at the last iteration in the Berlekamp-Massey-Sakata algor...

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Bibliographic Details
Published in:IEEE transactions on information theory 2021-01, Vol.67 (1), p.268-281
Main Authors: Bernal-Buitrago, Jose Joaquin, Simon-Pinero, Juan Jacobo
Format: Article
Language:English
Subjects:
Abelian codes
Algorithms
Berlekamp-Massey-Sakata algorithm
Decoding
Frequency modulation
Groebner basis
Indexes
Iterative decoding
Iterative methods
Jacobian matrices
linear recurring relations
Polynomials
Rings (mathematics)
Zirconium
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Summary:We study the problem of the computation of Groebner basis for the ideal of linear recurring relations of a doubly periodic array. We find a set of indexes such that, along with some conditions, guarantees that the set of polynomials obtained at the last iteration in the Berlekamp-Massey-Sakata algorithm is exactly a Groebner basis for the mentioned ideal. Then, we apply these results to improve locator decoding in abelian codes.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2020.3027751