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Efficient list decoder for algebraic-geometric codes

A list decoder can outperform the conventional unique decoder by giving a list of transmitted message candidates and can be applied to Reed-Solomon (RS) codes and algebraic-geometric (AG) codes. This paper presents the first efficient list decoder which is developed from the framework of the GuruswamiSudan (GS) algorithm for AG codes. Fast implementation methods for the algorithm’s key processes – interpolation and factorisation are also proposed. By applying this list decoder to the best performing AG codes, Hermitian codes, simulation results show that Hermitian codes defined over GF(64) can outperform similar code rate RS codes defined over GF(256) on the AWGN and Rayleigh fading channels, achieving up to a 4.05 dB coding gain using the same interpolation multiplicity.