分析了应用线性松弛方法对低密度奇偶校验(LDPC)码进行最大似然译码的基本原理,介绍了基于LDPC码校验矩阵因子图表达构造码字多胞形的方法。这些多胞形描述过于复杂,并且存在冗余,因此给出了一种简化约束条件。从接收正确码字必须服从校验方程出发,导出了以错误模式为变量、基于伴随式的LDPC码最大似然译码优化模型。
The basic principles of linear programming algorithm for the maximum likelihood decoding of LDPC codes are analyzed, and the ways to construct the codeword polytope based on the factor graph expression of parity check matrix of LDPC codes are described. Since these descriptions are too complex with redundancy, a simplified constraint description is introduced hereafter. Derived from the fact that the code word must be subordinate to check equations, an optimized model based on syndrome is obtained for the maximum likelihood decoding of LDPC codes.