Multi-session Network Coding Characterization Using New Linear Coding Frameworks

Han, Jaemin Ph.D., Purdue University, December 2013. Multi-session Network Coding Characterization using New Linear Coding Frameworks. Major Professor: ChihChun Wang Professor. Recently, Network Coding (NC) has emerged as a promising technique in modern communication networks and has shown extensive potentials in practical implementations and theoretical developments. Nevertheless, the NC problem itself remains largely open especially where the multiple flows (session) exist. Unlike single-session where all the receivers want the same information, they demand different information in multi-session and thus its NC strategy should be carefully designed to avoid interferences or sub-optimality. However, characterizing an optimal strategy has known to be of prohibitive complexity even we restrict to the linear network coding (LNC) problem. This thesis provides a fundamental approach to overcome this multi-session complexity. We considers the Directed Acyclic Wireline Networks, where people recently applied the results of wireless interference channels. Motivated by the graph-theoretic characterizations of classic linear NC results, we first propose a new Precoding-based Framework and its fundamental properties that bridge between the point-to-point network channel and the underlying graph structures. Such relationships turn out to be critical when characterizing graph-theoretically the feasibility of precoding-based solutions. One example of the applications of our results is to answer the conjectures of the 3-unicast interference alignment technique and the corresponding graph-theoretic characterization conditions. For the future work, we plan to consider the LNC characterization problem on the Wireless Packet Erasure Channel (PEC). Unlike Wireline Networks, the linear NC