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 Title: A digital interface for wireless networks Author(s): Muralidhar, Anand Director of Research: Kumar, P.R. Doctoral Committee Chair(s): Kumar, P.R. Doctoral Committee Member(s): Hajek, Bruce; Moulin, Pierre; Coleman, Todd P. Department / Program: Electrical & Computer Eng Discipline: Electrical & Computer Engr Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): digital interface approximate capacity relay networks interference networks linear codes network coding Abstract: This dissertation addresses the problem of determining the capacity of wireless networks and how to operate them. Within this context we present results on Gaussian relay, interference, and multicast networks. Two new models for wireless networks are introduced here: the discrete network and the superposition network. As with a Gaussian network, one can construct either a discrete network or a superposition network. The discrete network is obtained by simply quantizing the received signals in the Gaussian model and by restricting the transmit signals to a finite alphabet. The superposition network, inspired by the Gaussian model, is a noiseless deterministic network, the inputs and outputs of the channels are discrete, and channel gains are signed integers. The capacity of a class of Gaussian relay networks and its corresponding discrete or superposition network is always within a bounded gap, where the gap is independent of channel gains or signal-to-noise ratio (SNR), and depends only on the number $M$ of nodes in the network. More importantly, a near-optimal coding strategy for either the discrete or the superposition network can be converted into a near-optimal coding strategy for the original Gaussian network. Hence, both these networks serve as near-optimal digital interfaces for operating the Gaussian network. The discrete network is obtained from a Gaussian network by simply quantizing the received signals and restricting transmitted signals to a certain finite precision. Since its signals are obtained from those of a Gaussian network and its transmissions are transmittable as-is on a Gaussian network, the discrete network provides a particularly simple quantization-based digital interface for operating layered Gaussian relay networks. These are relay networks in which the nodes are grouped into layers, and only nodes of one layer can transmit to the nodes of the next layer. The cut-set upper bounds on the capacities of the Gaussian and the discrete network are within an SNR-independent bounded gap of $O(M \log M)$ bits. Moreover, a simple linear network code is a near-optimal coding strategy for the discrete relay network, achieving all rates within $O(M^2)$ bits of its cut-set bound, where the bound is independent of channel gains or SNR. The linear code can be used as-is on the Gaussian network after quantizing its received signals. It achieves all rates within $O(M^2)$ bits of the capacity for Gaussian relay networks. The linear network code improves on existing approximately-optimal coding schemes for the relay network by virtue of its simplicity and robustness, and it explicitly connects wireline network coding with codes for Gaussian networks. The approximation of Gaussian networks by other previously proposed deterministic networks is also studied in this dissertation, and two main results are presented, one positive and the other negative. The gap between the capacity of a Gaussian relay network and a corresponding linear deterministic network can be unbounded. The key reasons are that the linear deterministic model fails to capture the phase of received signals, and there is a loss in signal strength in the reduction to a linear deterministic network. On the positive side, Gaussian relay networks with a single source-destination pair are indeed well approximated by the superposition network. The difference between the capacity of a Gaussian relay network and the corresponding superposition network is bounded by $O(M \log M)$ bits, where the gap is again independent of channel gains or SNR. As a corollary, multiple-input multiple-output (MIMO) channels cannot be approximated by the linear deterministic model but can be by the superposition model. A code for a Gaussian relay network can be designed from {\em any} code for the corresponding superposition network simply by pruning it, suffering no more than a rate loss of $O(M \log M)$ bits that is independent of SNR. Similar results hold for the $K \times K$ Gaussian interference network, MIMO Gaussian interference networks, MIMO Gaussian relay networks, and multicast networks, with the constant gap depending additionally on the number of antennas in case of MIMO networks. Issue Date: 2011-08-25 URI: http://hdl.handle.net/2142/26043 Rights Information: Copyright 2011 Anand Muralidhar Date Available in IDEALS: 2011-08-25 Date Deposited: 2011-08
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