Efficient Coding for Multi-source Networks using Gacs-Korner Common Information

Consider a multi-source multicast network coding problem with correlated sources. While the fundamental limits are known, achieving them, in general, involves a computational burden due to the complex decoding process. Efficient solutions, on the other hand, are by large based on source and network coding separation, thus imposing strict topological constraints on the networks which can be solved. In this work, we introduce a novel notion of separation of source and network coding using Gacs-Korner Common Information (CI). Unlike existing notions of separation, the sufficient condition for this separation to hold depends on the source structure rather than the network topology. Using the suggested separation scheme, we tackle the problem of multi-source multicast. We construct efficient, zero error source codes, and via properties of the CI completely characterize the resulting rate region. We then study the complexity of the end-to-end scheme.