On the Feasibility of Network Alignment for Three-Source Three-Destination Multiple Unicast Networks with Delays

Abstract: A transform approach to network coding was introduced by Bavirisetti et al. (arXiv:1103.3882v3 [cs.IT]) as a tool to view wireline networks with delays as $k$-instantaneous networks (for some large $k$). When the local encoding kernels (LEKs) of the network are varied with every time block of length $k > 1$, the network is said to use block time varying LEKs. In this work, we propose a Precoding Based Network Alignment (PBNA) scheme based on transform approach and block time varying LEKs for three-source three-destination multiple unicast network with delays (3-S 3-D MUN-D). In a recent work, Meng et al. (arXiv:1202.3405v1 [cs.IT]) reduced the infinite set of sufficient conditions for feasibility of PBNA in a three-source three-destination instantaneous multiple unicast network as given by Das et al. (arXiv:1008.0235v1 [cs.IT]) to a finite set and also showed that the conditions are necessary. We show that the conditions of Meng et al. are also necessary and sufficient conditions for feasibility of PBNA based on transform approach and block time varying LEKs for 3-S 3-D MUN-D.