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A new precoding-based intersession network coding (NC) scheme has recentlybeen proposed, which applies the interference alignment technique, originallydevised for wireless interference channels, to the 3-unicast problem ofdirected acyclic networks. The main result of this work is a graph-theoreticcharacterization of the feasibility of the 3-unicast interference alignmentscheme. To that end, we first investigate several key relationships between thepoint-to-point network channel gains and the underlying graph structure. Suchrelationships turn out to be critical when characterizing graph-theoreticallythe feasibility of precoding-based solutions.

Graph-Theoretic Characterization of The Feasibility of The Precoding-Based 3-Unicast Interference Alignment Scheme