Generation and Extension of Linear Network Coding at Different Multicast Rates

By studying the intrinsic mechanism of linear network coding, this paper proposes a concept of generation and extension between two coding schemes at different multicast rates. We find out that a coding scheme at lower multicast rate is a generation of one at higher multicast rate,and a coding scheme at higher multicast rate is an extension of one at lower multicast rate. Moreover, we find out a determinate relationship between channelspsila global encoding vectors under two generation-extension coding schemes. Furthermore, by combining with random linear network coding, several important properties are derived, which are helpful to implement linear network coding for single-source multicast network. Some related applications are enumerated.