Soft-decision list decoding of hermitian codes
Soft-decision list decoding of hermitian codes
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DOI：
10.1109/tcomm.2009.08.070302
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发表时间：
2009-08
影响因子：
8.3
通讯作者：
Li Chen;R. Carrasco;M. Johnston
中科院分区：
文献类型：
--
作者：
Li Chen;R. Carrasco;M. Johnston
本文在Koetter-Vardy的Reed-Solomon码译码算法的基础上，提出了第一个完整的Hermitian码软判决列表译码算法。对于埃尔米特码，插值处理在埃尔米特曲线的极点基础上定义的三变量多项式。在本文中，重新定义了关于重数矩阵M的三变量多项式的内插零条件，随后证明了软决策方案的有效性。本文还介绍了将可靠性矩阵 Pi 转换为重数矩阵 M 的算法的新停止准则。研究了三变量单项式解码区域的几何特征，从而得出软决策解码器的渐近最优性能界限。通过定义插值多项式的加权次数上限，为软决策方案引入了两种降低复杂性的修改：消除不必要的插值多项式以及预先计算将极基单项式与埃尔米特曲线的零基函数相关的系数。我们的仿真结果和分析表明，埃尔米特码的软决策列表解码可以优于在较大有限域中定义的里德所罗门码的Koetter-Vardy解码，但解码复杂度较低。
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 Pi 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.