etd@IISc Collection:http://hdl.handle.net/2005/192018-01-25T20:49:11Z2018-01-25T20:49:11ZFast Solvers for Integtral-Equation based Electromagnetic SimulationsDas, Arkaprovohttp://hdl.handle.net/2005/29982018-01-10T01:59:03Z2018-01-09T18:30:00ZTitle: Fast Solvers for Integtral-Equation based Electromagnetic Simulations
Authors: Das, Arkaprovo
Abstract: With the rapid increase in available compute power and memory, and bolstered by the advent of efficient formulations and algorithms, the role of 3D full-wave computational methods for accurate modelling of complex electromagnetic (EM) structures has gained in significance. The range of problems includes Radar Cross Section (RCS) computation, analysis and design of antennas and passive microwave circuits, bio-medical non-invasive detection and therapeutics, energy harvesting etc. Further, with the rapid advances in technology trends like System-in-Package (SiP) and System-on-Chip (SoC), the fidelity of chip-to-chip communication and package-board electrical performance parameters like signal integrity (SI), power integrity (PI), electromagnetic interference (EMI) are becoming increasingly critical. Rising pin-counts to satisfy functionality requirements and decreasing layer-counts to maintain cost-effectiveness necessitates 3D full wave electromagnetic solution for accurate system modelling.
Method of Moments (MoM) is one such widely used computational technique to solve a 3D electromagnetic problem with full-wave accuracy. Due to lesser number of mesh elements or discretization on the geometry, MoM has an advantage of a smaller matrix size. However, due to Green's Function interactions, the MoM matrix is dense and its solution presents a time and memory challenge. The thesis focuses on formulation and development of novel techniques that aid in fast MoM based electromagnetic solutions.
With the recent paradigm shift in computer hardware architectures transitioning from single-core microprocessors to multi-core systems, it is of prime importance to parallelize the serial electromagnetic formulations in order to leverage maximum computational benefits. Therefore, the thesis explores the possibilities to expedite an electromagnetic simulation by scalable parallelization of near-linear complexity algorithms like Fast Multipole Method (FMM) on a multi-core platform.
Secondly, with the best of parallelization strategies in place and near-linear complexity algorithms in use, the solution time of a complex EM problem can still be exceedingly large due to over-meshing of the geometry to achieve a desired level of accuracy. Hence, the thesis focuses on judicious placement of mesh elements on the geometry to capture the physics of the problem without compromising on accuracy- a technique called Adaptive Mesh Refinement. This facilitates a reduction in the number of solution variables or degrees of freedom in the system and hence the solution time.
For multi-scale structures as encountered in chip-package-board systems, the MoM formulation breaks down for parts of the geometry having dimensions much smaller as compared to the operating wavelength. This phenomenon is popularly known as low-frequency breakdown or low-frequency instability. It results in an ill-conditioned MoM system matrix, and hence higher iteration count to converge when solved using an iterative solver framework. This consequently increases the solution time of simulation. The thesis thus proposes novel formulations to improve the spectral properties of the system matrix for real-world complex conductor and dielectric structures and hence form well-conditioned systems. This reduces the iteration count considerably for convergence and thus results in faster solution.
Finally, minor changes in the geometrical design layouts can adversely affect the time-to-market of a commodity or a product. This is because the intermediate design variants, in spite of having similarities between them are treated as separate entities and therefore have to follow the conventional model-mesh-solve workflow for their analysis. This is a missed opportunity especially for design variant problems involving near-identical characteristics when the information from the previous design variant could have been used to expedite the simulation of the present design iteration. A similar problem occurs in the broadband simulation of an electromagnetic structure. The solution at a particular frequency can be expedited manifold if the matrix information from a frequency in its neighbourhood is used, provided the electrical characteristics remain nearly similar. The thesis introduces methods to re-use the subspace or Eigen-space information of a matrix from a previous design or frequency to solve the next incremental problem faster.2018-01-09T18:30:00ZFunctional Index Coding, Network Function Computation, and Sum-Product Algorithm for Decoding Network CodesGupta, Anindyahttp://hdl.handle.net/2005/29992018-01-10T02:17:33Z2018-01-09T18:30:00ZTitle: Functional Index Coding, Network Function Computation, and Sum-Product Algorithm for Decoding Network Codes
Authors: Gupta, Anindya
Abstract: Network coding was introduced as a means to increase throughput in communication networks when compared to routing. Network coding can be used not only to communicate messages from some nodes in the network to other nodes but are also useful when some nodes in a network are interested in computing some functions of information generated at some other nodes. Such a situation arises in sensor networks. In this work, we study three problems in network coding.
First, we consider the functional source coding with side information problem wherein there is one source that generates a set of messages and one receiver which knows some functions of source messages and demands some other functions of source messages. Cognizant of the receiver's side information, the source aims to satisfy the demands of the receiver by making minimum number of coded transmissions over a noiseless channel. We use row-Latin rectangles to obtain optimal codes for a given functional source coding with side information problem. Next, we consider the multiple receiver extension of this problem, called the functional index coding problem, in which there are multiple receivers, each knowing and demanding disjoint sets of functions of source messages. The source broadcasts coded messages, called a functional index code, over a noiseless channel. For a given functional index coding problem, the restrictions the demands of the receivers pose on the code are represented using the generalized exclusive laws and it is shown that a code can be obtained using the confusion graph constructed using these laws. We present bounds on the size of an optimal code based on the parameters of the confusion graph. For the case of noisy broadcast channel, we provide a necessary and sufficient condition that a code must satisfy for correct decoding of desired functions at each receiver and obtain a lower bound on the length of an error-correcting functional index code.
In the second problem, we explore relation between network function computation problems and functional index coding and Metroid representation problems. In a network computation problem, the demands of the sink nodes in a directed acyclic multichip network include functions of the source messages. We show that any network computation problem can be converted into a functional index coding problem and vice versa. We prove that a network code that satisfies all the sink demands in a network computation problem exists if and only if its corresponding functional index coding problem admits a functional index code of a specific length. Next, we establish a relation between network computation problems and representable mastoids. We show that a network computation problem in which the sinks demand linear functions of source messages admits a scalar linear solution if and only if it is matricidal with respect to a representable Metroid whose representation fulfils certain constraints dictated by the network computation problem.
Finally, we study the usage of the sum-product (SP) algorithm for decoding network codes. Though lot of methods to obtain network codes exist, the decoding procedure and complexity have not received much attention. We propose a SP algorithm based decoder for network codes which can be used to decode both linear and nonlinear network codes. We pose the decoding problem at a sink node as a marginalize a product function (MPF) problem over the Boolean smearing and use the SP algorithm on a suitably constructed factor graph to perform decoding. We propose and demonstrate the usage of trace back to reduce the number of operations required to perform SP decoding. The computational complexity of performing SP decoding with and without trace back is obtained. For nonlinear network codes, we define fast decidability of a network code at sinks that demand all the source messages and identify a sufficient condition for the same. Next, for network function computation problems, we present an MPF formulation for function computation at a sink node and use the SP algorithm to obtain the value of the demanded function.2018-01-09T18:30:00ZWide-Band Radio-Frequency All-Pass Networks for Analog Signal ProcessingKeerthan, Phttp://hdl.handle.net/2005/30042018-01-10T03:46:06Z2018-01-09T18:30:00ZTitle: Wide-Band Radio-Frequency All-Pass Networks for Analog Signal Processing
Authors: Keerthan, P
Abstract: There is an ever increasing demand for higher spectral usage in wireless communication, radar and imaging systems. Higher spectral eﬃciency can be achieved using components that are aware of system environment and adapt suitably to the operating conditions. In this regard, radio frequency (RF) signal analysis is of paramount interest. Emergence of dispersive delay networks (DDN) has led to the significant development of microwave analogue-signal processing (ASP) and analysis. DDN causes displacement of spectral components in time domain, relative to the frequency dependant group delay response. The main challenge in the design of DDN in this context is in achieving broad bandwidth with high group delay dispersion (GDD). In this regard, all-pass networks (APN) have been explored as a potential wide-band DDN owing to the possibility of controlling the magnitude of loss characteristics without aﬀecting the dispersion in group delay response. The synthesis procedure of lumped element APN using approximation methods is well known at audio frequencies. Most of these use operational amplifier and cannot be extended directly to RF. There is no generalised closed form analytical procedure at RF for the synthesis of APN with the required GDD. In this regard, this dissertation presents the design and implementation of all-pass networks as wide-band dispersive delay networks at radio frequencies.
In this work, we begin by analysing the signal propagation through a DDN with a linear group delay response over a broad bandwidth. It is found that the signal experiences expansion of pulse width, reduction of its peak amplitude and a temporal displacement of the spectral components. Analytical expressions derived help initial synthesis of group delay response required for various ASP applications.
As the first step towards implementation at RF, a single stage APN is designed using surface mount devices (SMD). This design approach takes into account practical issues such as parasitic due to mounting pads, available component values, physical dimensions, self-resonance frequency (SRF) and finite Q factor of the components used. Full wave simulation of the design with transmission line pads and components is carried out. This implementation is useful for frequencies up to the component SRF, generally about 5 GHz. This design approach makes the circuit footprint independent of frequency and the performance is limited only by the Q factor of the adopted technology. The Q factor aﬀects the loss characteristics with a negligible eﬀect on group delay response in the frequency band of interest.
In order to extend the APN design for high group delay, a novel board level implementation is developed consisting of both lumped SMD components and distributed elements. The implementation results in a lower sensitivity of group delay performance to the commercially specified component value tolerances than the approach using all SMD components. It has been experimentally verified that the measured group delay is 2.4 ns at 1.85 GHz, which is thrice that reported in other approaches. The implementation has a reduced circuit footprint and is attractive in practical applications as it is a single layer micro strip realisation with less complex fabrication procedure and fewer components to assemble.
As an extension of this towards wideband cascaded APN, an iterative design procedure is developed to achieve a monotonous group delay response over a broad bandwidth. The approach facilitates cascading of multiple stages of lumped APN with diﬀerent resonance frequency and peak group delay to obtain linear and non-linear group delay responses with both positive and negative GDD. Circuits with both positive and negative GDD are required for various ASP applications such as compressive receivers and the present approach is unique in obtaining both the responses, not possible with many other RF dispersion techniques. Circuit models have been simulated by cascading transfer function responses of the individual APNs. The design is further extended for SMD implementation.
To validate the above approach, a two stage APN is designed in the frequency range [0.5 - 1] GHz for a linear GDD of ±6 ns/GHz. Two negative GDD APNs are further cascaded to obtain a four stage implementation with an overall GDD of -12 ns/GHz. The experimental results are compared with full wave simulations for validation. The design using lumped SMD components has greatly improved the performance in terms of GDD with a reduced circuit footprint and lower insertion loss than previously reported approaches.
As practical examples, the ASP modules are experimentally demonstrated using the fabricated APN. Frequency discrimination of two input frequencies with a frequency resolution of 500 MHz is demonstrated. Higher GDD results in higher separation of frequency components in time domain. Pulse compression and magnification is also demonstrated for diﬀerent wideband LFM input signals. The dispersion eﬀects of amplitude reduction, pulse width expansion and frequency chirping are thereby validated experimentally.
In summary, the approaches presented in this dissertation enable the design of wideband all-pass networks to introduce dispersion delays over wide bandwidths, opening up the possibility for their use in analogue signal processing at radio frequencies. Some of these applications have been experimentally demonstrated and validated using time frequency analysis.2018-01-09T18:30:00ZRole of Nonlocality and Counterfactuality in Quantum CryptographyAkshatha Shenoy, Hhttp://hdl.handle.net/2005/29872018-01-09T01:55:24Z2018-01-08T18:30:00ZTitle: Role of Nonlocality and Counterfactuality in Quantum Cryptography
Authors: Akshatha Shenoy, H
Abstract: Quantum cryptography is arguably the most successfully applied area of quantum information theory. In this work, We invsetigate the role of quantum indistinguishability in random number
generation, quantum temporal correlations, quantum nonlocality and counterfactuality for quantum cryptography. We study quantum protocols for key distribution, and their security in the conventional setting, in the counterfactual paradigm, and finally also in the device-independent scenario as applied to prepare-and-measure schemes.
We begin with the interplay of two essential non-classical features like quantum indeterminism and quantum indistinguishability via a process known as bosonic stimulation is discussed. It
is observed that the process provides an efficient method for macroscopic extraction of quantum randomness.
Next, we propose two counterfactual cryptographic protocols, in which a secret key bit is generated even without the physical transmission of a particle. The first protocol is semicounterfactual in the sense that only one of the key bits is generated using interaction-free
measurement. This protocol departs fundamentally from the original counterfactual key distribution protocol in not encoding secret bits in terms of photon polarization. We discuss how the security in the protocol originates from quantum single-particle non-locality. The second protocol is designed for the crypto-task of certificate authorization, where a trusted third party authenticates an entity (e.g., bank) to a client. We analyze the security of both protocols under various general incoherent attack models.
The next part of our work includes study of quantum temporal correlations. We consider the use of the Leggett-Garg inequalities for device-independent security appropriate for prepare-and-measure protocols subjected to the higher dimensional attack that would completely undermine standard BB84.
In the last part, we introduce the novel concept of nonlocal subspaces constructed using the graph state formalism, and propose their application for quantum information splitting. In particular, we use the stabilizer formalism of graph states to construct degenerate Bell operators,
whose eigenspace determines the nonlocal subspace, into which a quantum secret is encoded and shared among an authorized group of agents, or securely transmitted to a designated secret retriever. The security of our scheme arises from the monogamy of quantum correlations. The quantum violation of the Bell-type inequality here is to its algebraic maximum, making this approach inherently suitable for the device-independent scenario.2018-01-08T18:30:00Z