Analysis of Precoding-Based Intersession Network Coding and the Corresponding 3-Unicast Interference Alignment Scheme
Recently, a new pre-coding-based intersession Network Coding (NC) scheme has been proposed, which applies the interference alignment technique, originally devised for wireless interference channels, to the 3-unicast problem of directed acyclic networks. Motivated by the graph-theoretic characterizations of classic linear NC results, this paper investigates several key relationships between the point-to-point network channel gains and the underlying graph structure. Such relationships are critical when characterizing graph-theoretically the feasibility of pre-coding-based solutions. One example of the applications of their results is to answer (at least partially) the conjectures of the 3-unicast interference alignment technique and the corresponding graph-theoretic characterization conditions.