Journal of Symbolic Computation
Codes and algebraic curves
List Decoding of Error-Correcting Codes: Winning Thesis of the 2002 ACM Doctoral Dissertation Competition (Lecture Notes in Computer Science)
Enhancing WLAN/UMTS Dual-Mode Services Using a Novel Distributed Multi-Agent Scheduling Scheme
ISCC '06 Proceedings of the 11th IEEE Symposium on Computers and Communications
Reduced Complexity Interpolation for List Decoding Hermitian Codes
IEEE Transactions on Wireless Communications - Part 1
Fast decoding of algebraic-geometric codes up to the designed minimum distance
IEEE Transactions on Information Theory - Part 1
IEEE Transactions on Information Theory
Improved decoding of Reed-Solomon and algebraic-geometry codes
IEEE Transactions on Information Theory
Efficient decoding of Reed-Solomon codes beyond half the minimum distance
IEEE Transactions on Information Theory
Efficient root-finding algorithm with application to list decoding of algebraic-geometric codes
IEEE Transactions on Information Theory
Algebraic soft-decision decoding of Reed-Solomon codes
IEEE Transactions on Information Theory
Improved probabilistic decoding of interleaved Reed-Solomon codes and folded Hermitian codes
Theoretical Computer Science
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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 Π 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.