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Soft-Decision List Decoding of Hermitian Codes

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



This paper proposes the first complete soft-decision list decoding algorithm for Hermitian codes based on the Koetter-Vardy's Reed-Solomon code decoding algorithm. For Hermitian codes, interpolation processes trivariate polynomials which are defined over the pole basis of a Hermitian curve. In this paper, the interpolated zero condition of a trivariate polynomial with respect to a multiplicity matrix M is redefined followed by a proof of the validity of the soft-decision scheme. This paper also introduces a new stopping criterion for the algorithm that tranforms the reliability matrix H to the multiplicity matrix M. Geometric characterisation of the trivariate monomial decoding region is investigated, resulting in an asymptotic optimal performance bound for the soft-decision decoder. By defining the weighted degree upper bound of the interpolated polynomial, two complexity reducing modifications are introduced for the soft-decision scheme: elimination of unnecessary interpolated polynomials and pre-calculation of the coefficients that relate the pole basis monomials to the zero basis functions of a Hermitian curve. Our simulation results and analyses show that soft-decision list decoding of Hermitian code can outperform Koetter-Vardy decoding of Reed-Solomon code which is defined in a larger finite field, but with less decoding complexity.

Publication metadata

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

Publication type: Article

Publication status: Published

Journal: IEEE Transactions on Communications

Year: 2009

Volume: 57

Issue: 8

Pages: 2169-2176

ISSN (print): 0090-6778

ISSN (electronic): 1558-0857

Publisher: IEEE


DOI: 10.1109/TCOMM.2009.08.070302


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