线性网络编码的类型保持转换矩阵

提出了类型保持转换矩阵的概念，用以描述为同一网络构建的类型相同、速率不同的线性网络编码间的转换关系，并为四类线性网络编码证明了其类型保持转换矩阵的存在性。进而，提出了一种变速率线性网络编码的构建框架。当在网络上实现由此框架构建的任意类型的变速率线性网络编码时，仅信源节点需要根据发送速率的变化采用相应的类型保持转换矩阵改变其局部编码核，而网络中任意非源节点上进行的网络编码操作均无需改变。

Type-preserving conversion matrix for linear network codes

The concept of type-preserving conversion matrix is proposed to describe the conversion relationship between two linear network codes of the same type but of different rates.Its existence is proved for all four types of linear network codes.Then,a unified framework for the constructions of all four types of variable-rate linear network codes is proposed.To implement variable-rate network codes of any type constructed by this framework,every non-source node in the network needs to store only one local encoding kernel.When the transmission rate varies,only the source node needs to change it local encoding kernel with corresponding type-preserving conversion matrix,while the network-coding operations performed at every non-source node remain unchanged.