| Network coding in wired networks has been shown to achieve considerable throughput gains relative to traditional routing networks. In wireless networks, Galois-field network coding (GFNC) has been explored over the last years. However, the throughput of GFNC-based networks does not scale well as the number of sources increases, which motivates the complex field network coding (CFNC) approach in this thesis. CFNC achieves higher throughput than GFNC in a multi-source network while enabling the full diversity gain provided by the distributed multi-input multi-output (MIMO) channel regardless of the underlying signal-to-noise-ratio (SNR) and the constellation used. A link-adaptive regeneration relaying strategy is also developed for CFNC to achieve full diversity with or without error control coding.;With the help of a relay, CFNC also allows n nodes exchanging information with simultaneous transmissions from multiple sources in a wireless network. Although the ergodic capacity is unknown for wireless multihop networks, the scaling of capacity with the number of nodes (n) has recently received increasing attention. While existing works mainly focus on networks with n source-destination pairs, this thesis deals with capacity scaling in any-to-any wireless links, where each node communicates with all other nodes. As n increases, a hierarchical CFNC-based scheme is developed and shown to achieve asymptotically optimal quadratic capacity scaling in a dense network, where the area is fixed and the density of nodes increases. This is possible by dividing the network into many clusters, with each cluster sub-divided into many sub-clusters, hierarchically. As a result, information is transmitted on MIMO based multiple access channels and broadcast channels. When generalized to extended networks, where the density of nodes is fixed and the area increases linearly with n, the hierarchical CFNC scheme is shown to scale as n 3--alpha/2 for a path loss exponent alpha ≥ 2, which is asymptotically optimal when alpha < 3.;While a relay node improves the throughput, a jammer node may be present to inhibit or halt the transmission of signals in a tactical (or commercial) wireless network. A two-person zero-sum mutual information game is considered between one jammer ( J ) and one relay ( R ), in both non-fading and fading scenarios. |
