Analysis and design of multi-session network coding

Abstract

This thesis is devoted to analyzing the network coding capacity and constructing explicit network codes for various types of multi-session networks. First, to simplify the analysis of network coding capacity, some systematic graph reduction techniques are developed to reduce the order of the functional dependence graph of a network, hence the related outer bounds, such as the linear programming bound and functional dependence bound, can be computed with much less complexity. Furthermore, based on the functional dependence relationship of the source/edge variables, a lower bound on the mutual information between any two subsets of source/edge variables are presented, which renders a class of tighter functional dependence bounds on network coding capacity with different rate weights. On the other hand, explicit linear network coding schemes are proposed for double-unicast networks, which achieves a strictly larger rate region than the existing schemes, then a joint routing and network coding scheme is proposed to further enlarge the rate region. Finally, the throughput for erasure networks with spatial-temporal network coding is derived as a function of the temporal coding length. The derived expression is useful for the design and dimensioning of practical networks which can only have finite coding lengths.