摘要
译码作为编码理论中的一个重要过程,算法的优劣直接决定信息的处理速度。叙述了如何将Grbner基方法用在译码过程的计算中以提高译码效率。首先,介绍了Grbner基和译码过程中的相关理论。然后,分析了纠错码的译码过程并导出伴随式方程组,即多项式方程组。因为变元字典序的Grbner基具有消元的性质,故译码时使用字典序的Grbner基求解得到的方程组。利用了Grbner基求解非线性代数方程组的高效性。该方法具有很强的通用性。
Decoding plays important roles in coding theory,and whether its algorithm is good directly decides the efficiency of decoding system.We try to use Grbner bases theory in finite field to decode linear error-correcting codes.First,we revisit the elementary of Grbner bases.Then,analyze the relation between Grbner bases and algebra structure of syndrome.On the base of these,deduce nonlinear polynomial equations from the definition of syndrome.In the decoding,lexicographical Grbner bases are used to solve the equations,which including the syndrome equation and constraint conditions.This method takes advantage of the high efficiency of solving nonlinear polynomial equations by using Grbner bases.It is general in the decoding and can improve the speed of decoding remarkably.
出处
《武汉理工大学学报》
CAS
CSCD
北大核心
2010年第20期51-54,60,共5页
Journal of Wuhan University of Technology
基金
天津工程师范学院引进人才基金(KYQD06005)
关键词
Grbner基
纠错码
译码
Grbner bases
error-correcting codes
decoding
