The universal approximation theorem states that any regular function can be approximated closely using a single hidden layer neural network. Some recent work has shown that, for some special functions, the number of nodes in such an approximation could be exponentially reduced with multi-layer neural networks. In this work, we extend this idea to a rich class of functions, namely the discriminant functions that arise in optimal Bayesian classification of Gaussian mixture models (GMMs) in $\mathds{R}^n$. We show that such functions can be approximated with arbitrary precision using $O(n)$ nodes in a neural network with two hidden layers (deep neural network), while in contrast, a neural network with a single hidden layer (shallow neural network) would require at least $O(\exp(n))$ nodes or exponentially large coefficients. Given the universality of the Gaussian distribution in the feature spaces of data, e.g., in speech, image and text, our results shed light on the observed efficiency of deep neural networks in practical classification problems.

We extend studies on power optimization in VDSL2 to G.fast, the technology under definition. In vectored G.fast the power of the signals before precoding needs to be optimized to meet power spectral density and maximum aggregate transmit power constraints per line. We formulate this interplay between vectoring and power optimization, with non-vectored transmission as a particular case. Three power allocation algorithms are devised that allow a tradeoff between optimality and computational complexity. Measured channel data from a European operator up to 106 MHz is considered. Numerical evaluation reveals that low complex heuristics for power optimization yield near optimal solutions both with perfect and imperfect channel state information. Similar conclusions hold for the 212 MHz profile.

Intermittent transmission through low power states and discontinuous operation has been introduced in G.fast to enhance energy efficiency. In combination with vectoring, crosstalk cancellation must be maintained on active lines while other lines are in discontinuous operation. Without precautions, the requirements of vectoring may greatly reduce the power saving potential. We describe methods that allow trading off some of the vectoring gain for additional power saving. Using an energy consumption model, we evaluate the energy/rate trade-off of the methods under various traffic profiles. The method called discontinuous vectoring greatly enhances energy efficiency while incurring smaller data rate loss compared to other methods.

We present a measurement study of the energy consumption of an operator-side digital subscriber line (DSL) board under various conditions of data rate and power spectral density, with and without vectoring. The results highlight practical opportunities and challenges for optimizing rate-power-stability tradeoffs in DSL access systems, complementing simulation-based studies focused on energy reduction through spectral optimization. We validate models for line board consumption that can be tied with line driver consumption based on the aggregate transmit power of each line, and demonstrate that near-optimal rate-power-stability tradeoffs can be obtained through external line management of data rate, Signal-to-Noise-Ratio margin and power spectral density parameters.

LTE is currently considered by many wireless operators as their next generation technology. During a transition phase, LTE will be deployed as an overlay on an existing wireless technology, which acts as an underlay. It is expected that initial LTE deployment will be patchy with coverage holes. In this paper, we model and analyze the impact of dual-technology deployment on signaling load at critical network elements. We consider a case, known as without ISR, where a location update is executed when a UE moves between an overlay and an underlay and another case, known as with ISR, where a location update is made only when a new tracking area or routing area is encountered by a UE. Given a fixed total area of coverage holes in an overlay, our result shows that update rate increases as a square root of the number of coverage holes without ISR while it is virtually constant with ISR.

Rapid acquisition of accurate crosstalk estimates is a core requirement for effective preceding in digital subscriber line (DSL) systems. It is shown that signal-to-noise ratio (SNR) reports provided by customer premises equipment (CPE) can be used to perform this task by "tuning" the precoder, i.e., iterating alternate steps of estimation and precoder adaptation. Such an approach has the advantage that it can be applied to legacy CPEs. Estimation algorithms are designed using techniques from stochastic control.

In wireless networks, monotonic, strictly subhomogeneous functions have been used to analyze power control algorithms. We provide an alternative analysis based on the observation that such functions are shrinking with respect to certain metrics. These metrics are then used to analyze problems involving two classes of non-monotonic functions. The first class consists of normalized interference functions that can be used to compute the maximum achievable signal-to-interference ratio under power constraints. The second class consists of absolutely subhomogeneous functions that are used to approximate power control dynamics with outages. The eigensolutions of monotonic, strictly subhomogeneous functions are characterized as part of this development.

Time-domain Wavelength Interleaved Networking (TWIN) is a cost-effective network architecture that can provide fine-grained, flexible connectivity using passive optics in internal nodes. Each wavelength is dedicated to carry traffic to a single node. We introduce TWIN with wavelength reuse (TWIN-WR), an extension of TWIN that allows the number of nodes to exceed the number of wavelengths. We formulate an associated design problem, decompose it into subproblems, and provide algorithms for solving the subproblems. We experimentally demonstrate that our algorithms come close to upper bounds over a wide range of parameters, and show that the resulting designs are robust in the face of traffic variability and uncertainty. Analysis and experiment show that high efficiency can be maintained as long as the number of nodes does not exceed the square of the number of wavelengths, in principle allowing a network with thousands of nodes using only one hundred wavelengths.