Variable-rate, static and universal generic linear network codes

On an acyclic network, generic linear network codes are known to have the strongest optimality in terms of linear independence. This paper characterizes other properties of generic codes on a given acyclic network. We first show that every generic code is variable-rate generic with the additional property that the coding coefficients in relation to data-generating edges need not be changed. We next strengthen the concept of static generic codes to make the code preserve the generic property not only in the case of edge failures, but also in the case of adding some edges to be data-generating. Along this line, we define a new class of generic codes, called universal generic codes, such that the code is always generic with respect to any selection of data-generating edges. Last, we provide a unified characterization of static and universal generic codes on a given acyclic network in terms of the generic codes on an associated layered network.