Unique Decoding of General AG Codes

• Published in: IEEE transactions on information theory Vol. 60; no. 4; pp. 2038 - 2053
• Main Authors: Lee, Kwankyu, Bras-Amoros, Maria, O'Sullivan, Michael E.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2014; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: 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; Performance evaluation; Multicast; Interpolation; Multipoint AG code; Decoding; Gröbner base; Algorithm; Data broadcast; Information dissemination; Implementation; decoding algorithm
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2014.2306816

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.