On linear network coding

Many recent papers study methods, bounds and limitations for linear network coding. We examine prior definitions of linearity in network coding and show their implications in terms of code design and performance. We demonstrate how codes with one notion of linearity can be used to build, in a distributed manner, codes with another notion of linearity. One such reduction provides a simple construction for convolutional multicast network codes. We also provide examples of networks for which convolutional network code design is significantly less complex than for any block code. Finally, we introduce the new class of filter-bank network codes of which all previous definitions of linear network codes are special cases. This work is motivated by discussions with Dr. Ralf Koetter