Abstract
We consider a directed acyclic network with two source-sink pairs {s(1), t(1)} and {s(2), t(2)}. The source s(1) wishes to communicate a message X-1 to the sink t(1) and the source s(2) wishes to communicate two messages X-2 and X-3 to the sink t(2), where X-i, 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 {s(1), s(2)} to t(2) equals 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.