扩展卷积码生成矩阵的统一表述

A Unified Description of Generator Matrix of Expansion Convolutional Codes

针对在删除卷积码识别过程中缺乏对扩展卷积码先验认知的问题,提出了一种求解母码与扩展卷积码生成矩阵的统一表述方法。通过分析编码器输入输出关系的基本物理意义,先后以(n,1,m)、(n,k,m)作为母码,构建了其与扩展后编码器多项式系数的对应关系模型,归纳和证明了扩展卷积码生成矩阵的统一表述定理。验证结果表明:该定理能够对扩展卷积码生成矩阵实现快速计算,为遍历和重建删除卷积码的删除图样和母码生成矩阵提供方便。

In order to get enough priori knowledge about the expansion convolutional codes in the process of blind recognition of punctured convolutional codes,a method for describing the unified generator matrix of the mother code and the expansion convolutional codes is proposed. Through analyzing the basic physic principle of the relationship between the input and the output of encoding,the method first sets ( n,1,m) and( n,k,m) convolutional codes as the mother code,then constructs a correspondence coefficient model of the polymerization of the expansion convolutional coding,and finally introduces and proves a unified de-scription theorem about the generator matrix of the expansion convolutional codes. The verification shows that the theorem realizes the fast computation of the expansion generator matrix and is able to help to ex-haustively search and reconstruct the mother generator matrices and the puncturing patterns.