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In this thesis we study wireless networks modeled by the additive white Gaussian noise (AWGN) model. The AWGN capacity region of most network topologies is unknown, which means that the optimal transmission scheme is unknown as well. This motivates the search for capacity approximations and for approximately optimal schemes. Deterministic channel models have been proposed as means to approximate the AWGN model within a constant additive gap. We consider two particular models, the linear finite-field model (LFFM) and the discrete superposi- tion model (DSM). In the first part of the thesis we utilize the LFFM to design transmission schemes for layered relay networks in the AWGN model. We show that if a transmission scheme in the LFFM satisfies a certain set of coordination constraints, it can be translated to the AWGN model. A form of hierarchical modulation is used to build multiple transmission layers. By analyzing the performance in the AWGN model, we show that the AWGN rate is at most a constant gap below the LFFM rate. In the second part, we use the DSM to approximate the capacity and secrecy capacity of AWGN networks. First, we prove that the DSM capacity of some topologies is within a constant gap to the corresponding AWGN capacity. The topologies are given by the partially cognitive interference channel (PCIFC), a class of multiple-unicast networks, and a class of relay networks with secrecy con- straints, respectively. Then, we approximate the capacity in the DSM. We bound the capacity of the point-to-point channel, the capacity regions of the multiple- access channel and the broadcast channel, as well as the secrecy capacity of parallel relay networks (PRN) with an orthogonal eavesdropper and conventional relays. Furthermore, we find inner bounds on the capacity region of the PCIFC. This approach yields achievable rate regions for the PCIFC in the AWGN model and the AWGN secrecy capacity of the PRN within a constant gap. QC 20130516

QC 20140115

Wireless communication is commonly modeled as a stochastic system. This is justified by the fact that the wireless channel incorporates a number of stochastic effects including fading, interference and thermal noise.One example for a stochastic model is the additive white Gaussian noise (AWGN) model, which has been successfully used to analyze the capacity of the point-to-point channel and some multi-terminal networks. However, the AWGN capacity of most networks is still an open problem. This includes small examples like the relay channel, which consists of just three terminals.In order to progress, it was suggested to investigate deterministic channel models as an approximation of the AWGN model. The objective is to find a deterministic model, which is accessible to capacity analysis. Furthermore, this analysis should provide insights on the capacity of the AWGN model.In this thesis we consider two deterministic models, the linear finite-field model (LFFM) by Avestimehr et at. and the discrete superposition model (DSM) by Anand and Kumar.It has been shown that the capacity of the DSM is a constant gap approximation of the AWGN capacity for some networks including the parallel relay network (PRN). We find upper and lower bounds on the DSM capacity of the point-to-point channel, the multiple-access channel, the broadcast channel and the PRN. Our bounds are within a constant gap, hence, they yield a constant gap approximation to the AWGN capacity of the PRN.We also show how the LFFM can be utilized to design transmission strategies for AWGN relay networks. A transmission strategy in the LFFM can be translated into a transmission strategy in the AWGN model if it fulfills certain constraints. We consider two sets of constraints, and we show that in both cases the rate in the AWGN model is at most a constant below the rate in the corresponding LFFM. QC 20110407

This paper characterizes achievable rate regions for the Gaussian partially cognitive interference channel with multiple cognitive pairs ( $K$ -PCIFC), where the cognitive transmitters know one part of the primary transmitter's message. We explore a novel methodology using the deterministic discrete superposition model (DSM). We find codes and their achievable rate regions in the DSM, and we show that they yield achievable rate regions in the Gaussian model. Our coding scheme in the DSM can be applied in general scenarios. We devise an achievable rate region for the $K$ -PCIFC, which is within a constant gap to known outer bounds for $K=2$ in the weak interference regime. From our expressions we derive guidelines for designing the cognitive link between the primary transmitter and the cognitive transmitters. Furthermore, we show that the gain from cognition diminishes for increasing $K$ .