Network coding for two-unicast with rate (1,2)
Wentu Song, Rongquan Feng, Kai Cai, Junshan Zhang · 2012
We consider a directed acyclic network with two source-sink pairs {s1, t1} and {s2, t2}. The source s1wishes to communicate a message X1to the sink t1and the source s2wishes to communicate two messages X2and X3to the sink t2, where Xi, i = 1,2,3, are independent random variables of unit rate. We give a simple characterization for linear solvability of such networks under the condition that the minimum cut from {s1, s2} to t2equals 3. We develop a region decomposition method for proving this result, which we believe can be an effective approach for non-multicast network coding problem.