An Algebraic Method for Decoding q-ary Codes via Submodules of Z^n

An Algebraic Method for Decoding q-ary Codes via Submodules of Z^n

In this paper, by using a relation between binomial ideal and submodules of Z n in , a submodule associated with the integer programming (IP) problem is defined. By computing the reduced Gröbner basis (RGB) of the submodule, the decoding problem of non-binary q-ary codes is considered as an integer...

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Veröffentlicht in:IEEE communications letters 2014-05, Vol.18 (5), p.857-860
Hauptverfasser: Aliasgari, Malihe, Sadeghi, Mohammad-Reza
Format: Artikel
Sprache:eng
Schlagworte:
Complexity theory
Grobner basis
group code
integer programming
IP networks
Manganese
Maximum likelihood decoding
Vectors
Z-module
Zinc
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Zusammenfassung:In this paper, by using a relation between binomial ideal and submodules of Z n in , a submodule associated with the integer programming (IP) problem is defined. By computing the reduced Gröbner basis (RGB) of the submodule, the decoding problem of non-binary q-ary codes is considered as an integer program problem. Decoding complexity is investigated and the effective factors in complexity are also determined. Furthermore, an example of the decoding method for a 3-ary code is provided.
ISSN:1089-7798
1558-2558
DOI:10.1109/LCOMM.2014.030914.132773