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Reduced Complexity Interpolation for List Decoding Hermitian Codes

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

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Abstract

List decoding Hermitian codes using the Guruswami-Sudan (GS) algorithm can correct errors beyond half the designed minimum distance. It consists of two processes: interpolation and factorisation. By first defining a Hermitian curve, these processes can be implemented with an iterative polynomial construction algorithm and a recursive coefficient search algorithm respectively. To improve the efficiency of list decoding Hermitian codes, this paper presents two contributions to reduce the interpolation complexity. First, in order to simplify the calculation of a polynomial's zero condition during the iterative interpolation, we propose an algorithm to determine the corresponding coefficients between the pole basis monomials and zero basis functions of a Hermitian curve. Second, we propose a modified complexity reducing interpolation algorithm. This scheme identifies any unnecessary polynomials during iterations and eliminates them to improve the interpolation efficiency. Due to the above complexity reducing modifications, list decoding long Hermitian codes with higher interpolation multiplicity becomes feasible. This paper shows list decoding algorithm can achieve significant coding gain over the conventional unique decoding algorithm.

Publication metadata

Author(s): Chen L, Carrasco R, Johnston M

Publication type: Article

Publication status: Published

Journal: IEEE Transactions on Wireless Communications

Year: 2008

Volume: 7

Issue: 11

Pages: 4353-4361

Date deposited: 16/03/2010

ISSN (print): 1536-1276

ISSN (electronic): 1558-2248

Publisher: IEEE

URL: http://dx.doi.org/10.1109/T-WC.2008.070615

DOI: 10.1109/T-WC.2008.070615

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