On Constructive Multi-Source Network Coding

The multi-source network coding problem, where multiple multicast sessions with independent data share a network, is an open challenge. It is observed that random mixing is asymptotically optimal for a pollution-free multi-source network coding problem, where no receiver can be reached by a source it does not need. To handle pollution in a general network, a pollution-free network of tagged pipes is constructed. Each link is partitioned into tagged pipes; each tag is a subset of the sources. The content flowing in each pipe can only be a function of the sources indicated in the tag. The pipes are interconnected to form a pollution-free network. This constructive scheme gives rise to an achievability theorem for general multi-source network coding. For acyclic graphs, the fact that decoded information can be used in generating output is modelled via "helpers". This results in a stronger achievability theorem for acyclic graphs. Further incorporating the degree of freedom in adding receivers, an even stronger achievability theorem is derived