Network Coding for Wireless and Wired Networks: Design, Performance and Achievable Rates

Many point-to-point communication problems are relatively well understood in the literature. For example, in addition to knowing what the capacity of a point-to-point channel is, we also know how to construct codes that will come arbitrarily close to the capacity of these channels. However, we know very little about networks. For example, we do not know the capacity of the two-way relay channel which consists of only three transmitters. The situation is not so different in the wired networks except special cases like multicasting. To understand networks better, in this thesis we study network coding which is considered to be a promising technique since the time it was shown to achieve the single-source multicast capacity. First we design and analyze deterministic and random network coding schemes for a cooperative communication setup with multiple sources and destinations. We show that our schemes outperform conventional cooperation in terms of the diversity-multiplexing tradeoff (DMT). Specifically, it can offer the maximum diversity order at the expense of a slightly reduced multiplexing rate. We derive the necessary and sufficient conditions to achieve the maximum diversity order. We show that when the parity-check matrix for a systematic maximum distance separable (MDS) code is used as the network coding matrix, the maximum diversity is achieved. We present two ways to generate full-diversity network coding matrices: namely using the Cauchy matrices and the Vandermonde matrices. We also analyze a selection relaying scheme and prove that a multiplicative diversity order is possible with enough number of relay selection rounds. In addition to the above scheme for wireless networks, we also study wired networks, and apply network coding together with interference alignment. We consider networks with $K$ source nodes and $J$ destination nodes with arbitrary message demands. We first consider a simple network consisting of three source nodes and four destination nodes and show that each user can achieve a rate of one half. Then we extend the result for the general case which states that when the min-cut between each source-destination pair is one, it is possible to achieve a sum rate that is arbitrarily close to the min-cut between the source nodes whose messages are demanded and the destination node where the sum rate is the summation of all the demanded source message rates plus the biggest interferer\u27s rate