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Efficient factorisation algorithm for list decoding algebraic-geometric and Reed-Solomon codes

Lookup NU author(s): Dr Li Chen, Emeritus Professor Rolando Carrasco, Dr Martin Johnston, Dr Graeme Chester

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Abstract

The list decoding algorithm can outperform the conventional unique decoding algorithm by producing a list of candidate decoded messages. An efficient list decoding algorithm for Algebraic-Geometric (AG) codes and Reed-Solomon (RS) codes has been developed by Guruswami and Sudan, called the Guruswami-Sudan (GS) algorithm. The algorithm includes two steps: Interpolation and Factorisation. To implement interpolation, Koetter proposed an iterative polynomial construction algorithm for RS codes. By redefining a polynomial over algebraic function fields, Koetter’s algorithm can also be applied to AG codes. To implement factorisation, Roth and Ruckenstein proposed an efficient algorithm for RS codes and later Wu and Siegel extended it to AG codes. Following on from their previous work, we propose a more general factorisation algorithm which can be applied to both AG and RS codes. This algorithm avoids rational function quotient calculations required by Wu and Siegel’s algorithm, making it more efficient to implement. As well as employing this algorithm to list decode AG and RS codes this paper also presents the first simulation results evaluating the list decoding performance comparison between AG and RS codes of a similar code rate defined over the same finite field.


Publication metadata

Author(s): Chen L, Carrasco RA, Johnston M, Chester EG

Publication type: Conference Proceedings (inc. Abstract)

Conference Name: International Conference on Communications

Year of Conference: 2007

Pages: 851-856

Publisher: IEEE

URL: http://dx.doi.org/10.1109/ICC.2007.145

DOI: 10.1109/ICC.2007.145

Library holdings: Search Newcastle University Library for this item

ISBN: 1424403537


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