FTN multicarrier transmission based on tight Gabor frames

A multicarrier signal can be synthesized thanks to a symbol sequence and a Gabor family (i.e., a regularly time-frequency shifted version of a generator pulse). In this article, we consider the case where the signaling density is increased such that inter-pulse interference is unavoidable.Over an additive white Gaussian noise channel, we show that the signal-to-interference-plus-noise ratio is maximized when the transmitter and the receiver use the same tight Gabor frame. What is more, we give practical efficient realization schemes and show how to build tight frames based on usual generators. Theoretical and simulated bit-error-probability are given for a non-coded system using quadrature amplitude modulations. Such a characterization is then used to predict the convergence of a coded system using low-density parity-check codes. We also study the robustness of such a system to errors on the received bits in an interference cancellation context

Direct and Inverse Acoustic Scattering by a Combined Scatterer

This paper is concerned with the scattering problem of time-harmonic acoustic plane waves by a union of a crack and a penetrable inhomogeneous medium with compact support. The well-posedness of the direct problem is established by the variational method. An uniqueness result for the inverse problem is proved, that is, both the crack and the inhomogeneous medium can be uniquely determined by a knowledge of the far-field pattern for incident plane waves. The linear sampling method is employed to recover the location and shape of the combined scatterer. It is worth noting that we make the first step on reconstructing a mixed-type scatterer of a crack and an inhomogeneous medium by the linear sampling method

Content delivery over multi-antenna wireless networks

The past few decades have witnessed unprecedented advances in information technology, which have significantly shaped the way we acquire and process information in our daily lives. Wireless communications has become the main means of access to data through mobile devices, resulting in a continuous exponential growth in wireless data traffic, mainly driven by the demand for high quality content. Various technologies have been proposed by researchers to tackle this growth in 5G and beyond, including the use of increasing number of antenna elements, integrated point-to-multipoint delivery and caching, which constitute the core of this thesis. In particular, we study non-orthogonal content delivery in multiuser multiple-input-single-output (MISO) systems. First, a joint beamforming strategy for simultaneous delivery of broadcast and unicast services is investigated, based on layered division multiplexing (LDM) as a means of superposition coding. The system performance in terms of minimum required power under prescribed quality-of-service (QoS) requirements is examined in comparison with time division multiplexing (TDM). It is demonstrated through simulations that the non-orthogonal delivery strategy based on LDM significantly outperforms the orthogonal strategy based on TDM in terms of system throughput and reliability. To facilitate efficient implementation of the LDM-based beamforming design, we further propose a dual decomposition-based distributed approach. Next, we study an efficient multicast beamforming design in cache-aided multiuser MISO systems, exploiting proactive content placement and coded delivery. It is observed that the complexity of this problem grows exponentially with the number of subfiles delivered to each user in each time slot, which itself grows exponentially with the number of users in the system. Therefore, we propose a low-complexity alternative through time-sharing that limits the number of subfiles that can be received by a user in each time slot. Moreover, a joint design of content delivery and multicast beamforming is proposed to further enhance the system performance, under the constraint on maximum number of subfiles each user can decode in each time slot. Finally, conclusions are drawn in Chapter 5, followed by an outlook for future works.Open Acces

Partons as unique ground states of quantum Hall parent Hamiltonians: The case of Fibonacci anyons

We present microscopic, multiple Landau level, (frustration-free and positive semi-definite) parent Hamiltonians whose ground states, realizing different quantum Hall fluids, are parton-like and whose excitations display either Abelian or non-Abelian braiding statistics. We prove ground state energy monotonicity theorems for systems with different particle numbers, demonstrate S-duality in the case of toroidal geometry and establish an exact zero-energy mode counting. The emergent Entangled Pauli Principle, introduced in Phys. Rev. B 98, 161118(R) (2018) and which defines the "DNA" of the quantum Hall fluid, is behind the exact determination of the topological characteristics of the fluid, including charge and braiding statistics of excitations, and effective edge theory descriptions. When the closed-shell condition is satisfied, the densest (i.e., the highest density and lowest total angular momentum) zero-energy mode is a unique parton state. As a corollary, it follows that the Moore-Read Pfaffian and Read-Rezayi states (both of which may be expressed as linear combinations of parton-like states) cannot be densest ground states of two-body parent Hamiltonians. We conjecture, based on the algebra of polynomials in holomormorphic and anti-holomorphic complex variables, that parton-like states span the subspace of many-body wave functions with the two-body $M$-clustering property, that is, wave functions with $M$th-order coincidence plane zeroes. We illustrate our framework by presenting a parent Hamiltonian whose excitations are rigorously proven to be Fibonacci anyons and show how to extract the DNA of the fluid whose entanglement pattern manifests in the form of a matrix product state.Comment: 49 pages, 17 figure

Algorithms for Circuit Sizing in VLSI Design

One of the key problems in the physical design of computer chips, also known as integrated circuits, consists of choosing a  physical layout  for the logic gates and memory circuits (registers) on the chip. The layouts have a high influence on the power consumption and area of the chip and the delay of signal paths.  A discrete set of predefined layouts  for each logic function and register type with different physical properties is given by a library. One of the most influential characteristics of a circuit defined by the layout is its size. In this thesis we present new algorithms for the problem of choosing sizes for the circuits and its continuous relaxation,  and  evaluate these in theory and practice. A popular approach is based on Lagrangian relaxation and projected subgradient methods. We show that seemingly heuristic modifications that have been proposed for this approach can be theoretically justified by applying the well-known multiplicative weights algorithm. Subsequently, we propose a new model for the sizing problem as a min-max resource sharing problem. In our context, power consumption and signal delays are represented by resources that are distributed to customers. Under certain assumptions we obtain a polynomial time approximation for the continuous relaxation of the sizing problem that improves over the Lagrangian relaxation based approach. The new resource sharing algorithm has been implemented as part of the BonnTools software package which is developed at the Research Institute for Discrete Mathematics at the University of Bonn in cooperation with IBM. Our experiments on the ISPD 2013 benchmarks and state-of-the-art microprocessor designs provided by IBM illustrate that the new algorithm exhibits more stable convergence behavior compared to a Lagrangian relaxation based algorithm. Additionally, better timing and reduced power consumption was achieved on almost all instances. A subproblem of the new algorithm consists of finding sizes minimizing a weighted sum of power consumption and signal delays. We describe a method that approximates the continuous relaxation of this problem in polynomial time under certain assumptions. For the discrete problem we provide a fully polynomial approximation scheme under certain assumptions on the topology of the chip. Finally, we present a new algorithm for timing-driven optimization of registers. Their sizes and locations on a chip are usually determined during the clock network design phase, and remain mostly unchanged afterwards although the timing criticalities on which they were based can change. Our algorithm permutes register positions and sizes within so-called  clusters  without impairing the clock network such that it can be applied late in a design flow. Under mild assumptions, our algorithm finds an optimal solution which maximizes the worst cluster slack. It is implemented as part of the BonnTools and improves timing of registers on state-of-the-art microprocessor designs by up to 7.8% of design cycle time. </div