A Simple Necessary and Sufficient Condition for the Double Unicast Problem
The authors consider a directed acyclic network where there are two source-terminal pairs and the terminals needs to receive the symbols generated at the respective sources. Each source independently generates an I.I.D. random process over the same alphabet. Each edge in the network is error-free, delay-free, and can carry one symbol from the alphabet per use. They give a simple necessary and sufficient condition for being able to simultaneously satisfy the uni-cast requirements of the two source-terminal pairs at rate-pair using vector network coding. The condition is also sufficient for doing this using only "XOR" network coding and is much simpler compared to the necessary and sufficient conditions known from previous paper.