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We consider a Gaussian relay network, which has to protect the message from a powerful eavesdropper, which has the possibility of listening to the transmitted signals on orthogonal channels. The secrecy capacity of the Gaussian network is approximated by considering the corresponding network in the deterministic discrete superposition model. Upper and lower bounds on the secrecy capacity are found in terms of the deterministic model, which are potentially easier to evaluate. We perform this evaluation for the particular topology of the parallel relay network, where the relays form a parallel layer between the source and the destination. By analyzing the deterministic model, we approximate the secrecy capacity within a constant gap. The approximation can be expressed just in terms of the channel gains of the network. It is therefore possible to deduct that the simple scheme of hiding the transmitted signals in noise is approximately optimal. [ABSTRACT FROM PUBLISHER]

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 $K$. [ABSTRACT FROM AUTHOR]

In this paper we show how the recently proposed linear finite-field deterministic model (LFFM) can be used to design transmission strategies for the corresponding AWGN model of wireless relay networks. The transmission scheme in the AWGN model uses hierarchical modulation to transmit information on multiple layers. We show that a transmission strategy in the LFFM can be translated to the AWGN model if it is coordinated, that is, if the amount of interference is limited in a certain way. We consider two types of coordination, full and partial, with different restrictions on the transmission scheme. In both cases we show that the rate in the AWGN model is at most a constant gap below the rate in the LFFM, which provides a link between the models. Closed-form upper bounds on the gap are derived based on the analysis of noise and interference forwarding. The bounds are evaluated numerically, and the dependency on the system parameters and the parameters of coordination are discussed. The trade-off between full and partial coordination and the corresponding parameters are illustrated. [ABSTRACT FROM AUTHOR]