Achieving the information rate region for two sources two sinks network coding: An extended work

In single-source network coding, we are interested in characterizing the maximum rate at which information can be multicast from the source node to all the sink nodes, this is accomplished by the mean of Max-Flow-Min-Cut theorem. In multi-source network coding the problem is different and more complicated; we are interested in characterizing the information rate region and the capacity region. In this work, which is an extension to our previous work, we found the inner and outer bounds of information rate region for two sources two sinks network coding; we achieved these bounds by using the Max-Flow constraints. Our multicasting algorithm is based on decomposing the current problem to three sub-problems: a multicast network coding sub-problem and two multi-commodity flow sub-problems.