Vector Network Coding Algorithms

Abstract—We develop new algebraic algorithms for scalar and vector network coding. In vector network coding, the source multicasts information by transmitting vectors of length L, while intermediate nodes process and combine their incoming packets by multiplying them with L × L coding matrices that play a similar role as coding coefſcients in scalar coding. Our algorithms for scalar network jointly optimize the employed ſeld size while selecting the coding coefſcients. Similarly, for vector coding, our algorithms optimize the length L while designing the coding matrices. These algorithms apply both for regular network graphs as well as linear deterministic networks. I