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Lookup NU author(s): Dr Martin Johnston,
Emeritus Professor Rolando Carrasco
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Algebraic-geometric codes were developed by V D Goppa in 1981 and are a class of non-binary block codes constructed from an irreducible affine curve. They have impressive coding parameters, such as large code length and Hamming distance, and many codes can be constructed from just one class of curve. The authors have recently published simulation results for several Hermitian codes over the AWGN and Rayleigh fading channel, which are thought to be the first simulation results for algebraic-geometric codes to be published. In this paper, the construction and decoding of Hermitian codes are explained and the simulation results of several Hermitian codes are shown and compared with similar Reed Solomon codes. The results show that due to their increased code length, Hermitian codes outperform Reed Solomon codes over the AWGN and Rayleigh fading channel. If the decoding complexity could be reduced then algebraic-geometric codes would be suitable to replace Reed Solomon codes in many different applications.
Author(s): Johnston M, Carrasco RA
Publication type: Conference Proceedings (inc. Abstract)
Publication status: Published
Conference Name: Eighth IEEE International Symposium on Communication Theory and Applications (ISCTA'05)
Year of Conference: 2005
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