Unique Decoding of General AG Codes

A unique decoding algorithm for general AG codes, namely multipoint evaluation codes on algebraic curves, is presented. It is a natural generalization of the previous decoding algorithm which was only for one-point AG codes. As such, it retains the same advantages of fast speed, regular structure, a...

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Veröffentlicht in:	IEEE transactions on information theory 2014-04, Vol.60 (4), p.2038-2053
Hauptverfasser:	Lee, Kwankyu, Bras-Amoros, Maria, O'Sullivan, Michael E.
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Algorithms Applied sciences Coding, codes Decoding decoding algorithm Encoding Exact sciences and technology Gröbner base Information theory Information, signal and communications theory Interpolation Iterative decoding Materials Multipoint AG code Polynomials Signal and communications theory Systems, networks and services of telecommunications Telecommunications Telecommunications and information theory Transmission and modulation (techniques and equipments) Vectors
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Beschreibung
Zusammenfassung:	A unique decoding algorithm for general AG codes, namely multipoint evaluation codes on algebraic curves, is presented. It is a natural generalization of the previous decoding algorithm which was only for one-point AG codes. As such, it retains the same advantages of fast speed, regular structure, and direct message recovery. Upon this generalization, we add a technique from the Guruswami-Sudan list decoding that boosts the decoding speed significantly. Compared with other known decoding algorithms for general AG codes, it has a similar decoding performance and allows streamlined practical implementation by its simple and regular structure.
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2014.2306816