On Deterministic Models for Wireless Networks
Abstract: 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.
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