基于极大极小准则下的(n,k,m)卷积码识别

Recognition of (n,k,m) convolutional codes based on maximum and minimum criterion

针对现有识别方法仅适用于特定类型的卷积码,以及容错能力有待提高的问题,提出了一种基于改进门限沃尔什-哈达玛变换(Walsh-Hadamard transform,WHT)的(n,k,m)卷积码参数遍历识别方法。首先,将问题分为非系统和系统形式两种情况进行考虑,根据各自结构特点分别建立关于校验多项式的二元域方程,并建立二元假设;然后,遍历不同的参数组合并利用WHT求解对应方程,通过二元判决得到校验多项式,同时为提升方法的鲁棒性,采用极大极小准则对判决门限进行了改进。最后,利用校验多项式矩阵与生成多项式矩阵的正交关系求解生成多项式。仿真结果表明,该方法对各码率的卷积码均能有效识别,且抗误码性能优于传统方法。

Current recognition methods for convolutional codes are only applicable to a specific code rate, and fault tolerant performance needs to be improved as well. To solve this problem, a parameter method based on parameter traversal and improved threshold Walsh-Hadamard transform (WHT) is proposed. According to the coding structure, F(2) equations for check polynomials are established in both cases of nonsystematic and systematic codes, with binary hypothesis being established. By traversing the possible coding parameters and solving the equations via WHT, the correct check polynomials are determined through threshold decision, while the threshold is improved based on maximum and minimum criterion to enhance robustness at the same time. Finally, generator polynomials are calculated on the basis of orthogonal relationship between check matrix and generator matrix. Simulations verify the applicability of the proposed method, which has a better error resilient performance compared with current recognition methods.