论文标题
迈向组网络代码的操作定义
Towards an Operational Definition of Group Network Codes
论文作者
论文摘要
小组网络代码是线性代码的概括，在过去的十年中，它们已经看到了几项研究。在研究网络代码时，在称为局部编码函数的内部网络节点上执行的操作引起了重大关注。尽管对线性代码的局部编码函数有充分的理解（并且具有操作意义），但组网络代码没有类似的操作定义。为了弥合这一差距，我们研究了组网络代码与称为坐标线性（CWL）代码的代码家族之间的连接。 CWL代码概括线性代码，此外，可以在本地定义（即在操作上）。在这项工作中，我们从本地和全局编码的角度研究了CWL代码和组代码之间的联系。我们表明，Abelian组代码可以表示为CWL代码，因此，它们继承了操作定义。
Group network codes are a generalization of linear codes that have seen several studies over the last decade. When studying network codes, operations performed at internal network nodes called local encoding functions, are of significant interest. While local encoding functions of linear codes are well understood (and of operational significance), no similar operational definition exists for group network codes. To bridge this gap, we study the connections between group network codes and a family of codes called Coordinate-Wise-Linear (CWL) codes. CWL codes generalize linear codes and, in addition, can be defined locally (i.e., operationally). In this work, we study the connection between CWL codes and group codes from both a local and global encoding perspective. We show that Abelian group codes can be expressed as CWL codes and, as a result, they inherit an operational definition.
