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Description
Information divergence functions, such as the Kullback-Leibler divergence or the Hellinger distance, play a critical role in statistical signal processing and information theory; however estimating them can be challenge. Most often, parametric assumptions are made about the two distributions to estimate the divergence of interest. In cases where no parametric model fits the data, non-parametric density estimation is used. In statistical signal processing applications, Gaussianity is usually assumed since closed-form expressions for common divergence measures have been derived for this family of distributions. Parametric assumptions are preferred when it is known that the data follows the model, however this is rarely the case in real-word scenarios. Non-parametric density estimators are characterized by a very large number of parameters that have to be tuned with costly cross-validation. In this dissertation we focus on a specific family of non-parametric estimators, called direct estimators, that bypass density estimation completely and directly estimate the quantity of interest from the data. We introduce a new divergence measure, the $D_p$-divergence, that can be estimated directly from samples without parametric assumptions on the distribution. We show that the $D_p$-divergence bounds the binary, cross-domain, and multi-class Bayes error rates and, in certain cases, provides provably tighter bounds than the Hellinger divergence. In addition, we also propose a new methodology that allows the experimenter to construct direct estimators for existing divergence measures or to construct new divergence measures with custom properties that are tailored to the application. To examine the practical efficacy of these new methods, we evaluate them in a statistical learning framework on a series of real-world data science problems involving speech-based monitoring of neuro-motor disorders.
ContributorsWisler, Alan (Author) / Berisha, Visar (Thesis advisor) / Spanias, Andreas (Thesis advisor) / Liss, Julie (Committee member) / Bliss, Daniel (Committee member) / Arizona State University (Publisher)
Created2017
Description
This work details the bootstrap estimation of a nonparametric information divergence measure, the Dp divergence measure, using a power law model. To address the challenge posed by computing accurate divergence estimates given finite size data, the bootstrap approach is used in conjunction with a power law curve to calculate an asymptotic value of the divergence estimator. Monte Carlo estimates of Dp are found for increasing values of sample size, and a power law fit is used to relate the divergence estimates as a function of sample size. The fit is also used to generate a confidence interval for the estimate to characterize the quality of the estimate. We compare the performance of this method with the other estimation methods. The calculated divergence is applied to the binary classification problem. Using the inherent relation between divergence measures and classification error rate, an analysis of the Bayes error rate of several data sets is conducted using the asymptotic divergence estimate.
ContributorsKadambi, Pradyumna Sanjay (Author) / Berisha, Visar (Thesis director) / Bliss, Daniel (Committee member) / Electrical Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Lossy compression is a form of compression that slightly degrades a signal in ways that are ideally not detectable to the human ear. This is opposite to lossless compression, in which the sample is not degraded at all. While lossless compression may seem like the best option, lossy compression, which is used in most audio and video, reduces transmission time and results in much smaller file sizes. However, this compression can affect quality if it goes too far. The more compression there is on a waveform, the more degradation there is, and once a file is lossy compressed, this process is not reversible. This project will observe the degradation of an audio signal after the application of Singular Value Decomposition compression, a lossy compression that eliminates singular values from a signal’s matrix.
ContributorsHirte, Amanda (Author) / Kosut, Oliver (Thesis director) / Bliss, Daniel (Committee member) / Electrical Engineering Program (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
This thesis presents a code generation tool to improve the programmability of systolic array processors such as the Domain Adaptive Processor (DAP) that was designed by researchers at the University of Michigan for wireless communication workloads. Unlike application-specific integrated circuits, DAP aims to achieve high performance without trading off much on programmability and reconfigurability. The structure of a typical DAP code for each Processing Element (PE) is very different from any other programming language format. As a result, writing code for DAP requires the programmer to acquire processor-specific knowledge including configuration rules, cycle accurate execution state for memory and datapath components within each PE, etc. Each code must be carefully handcrafted to meet the strict timing and resource constraints, leading to very long programming times and low productivity. In this thesis, a code generation and optimization tool is introduced to improve the programmability of DAP and make code development easier. The tool consists of a configuration code generator, optimizer, and a scheduler. An Instruction Set Architecture (ISA) has been designed specifically for DAP. The programmer writes the assembly code for each PE using the DAP ISA. The assembly code is then translated into a low-level configuration code. This configuration code undergoes several optimizations passes. Level 1 (L1) optimization handles instruction redundancy and performs loop optimizations through code movement. The Level 2 (L2) optimization performs instruction-level parallelism. Use of L1 and L2 optimization passes result in a code that has fewer instructions and requires fewer cycles. In addition, a scheduling tool has been introduced which performs final timing adjustments on the code to match the input data rate.
ContributorsVipperla, Anish (Author) / Chakrabarti, Chaitali (Thesis advisor) / Bliss, Daniel (Committee member) / Akoglu, Ali (Committee member) / Arizona State University (Publisher)
Created2022
Description
QR decomposition (QRD) of a matrix is one of the most common linear algebra operationsused for the decomposition of a square
on-square matrix. It has a wide range
of applications especially in Multiple Input-Multiple Output (MIMO) communication
systems. Unfortunately it has high computation complexity { for matrix size of nxn,
QRD has O(n3) complexity and back substitution, which is used to solve a system
of linear equations, has O(n2) complexity. Thus, as the matrix size increases, the
hardware resource requirement for QRD and back substitution increases signicantly.
This thesis presents the design and implementation of a
exible QRD and back substitution accelerator using a folded architecture. It can support matrix sizes of
4x4, 8x8, 12x12, 16x16, and 20x20 with low hardware resource requirement.
The proposed architecture is based on the systolic array implementation of the
Givens algorithm for QRD. It is built with three dierent types of computation blocks
which are connected in a 2-D array structure. These blocks are controlled by a
scheduler which facilitates reusability of the blocks to perform computation for any
input matrix size which is a multiple of 4. These blocks are designed using two
basic programming elements which support both the forward and backward paths to
compute matrix R in QRD and column-matrix X in back substitution computation.
The proposed architecture has been mapped to Xilinx Zynq Ultrascale+ FPGA
(Field Programmable Gate Array), ZCU102. All inputs are complex with precision
of 40 bits (38 fractional bits and 1 signed bit). The architecture can be clocked at
50 MHz. The synthesis results of the folded architecture for dierent matrix sizes
are presented. The results show that the folded architecture can support QRD and
back substitution for inputs of large sizes which otherwise cannot t on an FPGA
when implemented using a
at architecture. The memory sizes required for dierent
matrix sizes are also presented.
on-square matrix. It has a wide range
of applications especially in Multiple Input-Multiple Output (MIMO) communication
systems. Unfortunately it has high computation complexity { for matrix size of nxn,
QRD has O(n3) complexity and back substitution, which is used to solve a system
of linear equations, has O(n2) complexity. Thus, as the matrix size increases, the
hardware resource requirement for QRD and back substitution increases signicantly.
This thesis presents the design and implementation of a
exible QRD and back substitution accelerator using a folded architecture. It can support matrix sizes of
4x4, 8x8, 12x12, 16x16, and 20x20 with low hardware resource requirement.
The proposed architecture is based on the systolic array implementation of the
Givens algorithm for QRD. It is built with three dierent types of computation blocks
which are connected in a 2-D array structure. These blocks are controlled by a
scheduler which facilitates reusability of the blocks to perform computation for any
input matrix size which is a multiple of 4. These blocks are designed using two
basic programming elements which support both the forward and backward paths to
compute matrix R in QRD and column-matrix X in back substitution computation.
The proposed architecture has been mapped to Xilinx Zynq Ultrascale+ FPGA
(Field Programmable Gate Array), ZCU102. All inputs are complex with precision
of 40 bits (38 fractional bits and 1 signed bit). The architecture can be clocked at
50 MHz. The synthesis results of the folded architecture for dierent matrix sizes
are presented. The results show that the folded architecture can support QRD and
back substitution for inputs of large sizes which otherwise cannot t on an FPGA
when implemented using a
at architecture. The memory sizes required for dierent
matrix sizes are also presented.
ContributorsKanagala, Srimayee (Author) / Chakrabarti, Chaitali (Thesis advisor) / Bliss, Daniel (Committee member) / Cao, Yu (Kevin) (Committee member) / Arizona State University (Publisher)
Created2020
Description
The following document describes the hardware implementation and analysis of Temporal Interference Mitigation using High-Level Synthesis. As the problem of spectral congestion becomes more chronic and widespread, Electromagnetic radio frequency (RF) based systems are posing as viable solution to this problem. Among the existing RF methods Cooperation based systems have been a solution to a host of congestion problems. One of the most important elements of RF receiver is the spatially adaptive part of the receiver. Temporal Mitigation is vital technique employed at the receiver for signal recovery and future propagation along the radar chain.
The computationally intensive parts of temporal mitigation are identified and hardware accelerated. The hardware implementation is based on sequential approach with optimizations applied on the individual components for better performance.
An extensive analysis using a range of fixed point data types is performed to find the optimal data type necessary.
Finally a hybrid combination of data types for different components of temporal mitigation is proposed based on results from the above analysis.
The computationally intensive parts of temporal mitigation are identified and hardware accelerated. The hardware implementation is based on sequential approach with optimizations applied on the individual components for better performance.
An extensive analysis using a range of fixed point data types is performed to find the optimal data type necessary.
Finally a hybrid combination of data types for different components of temporal mitigation is proposed based on results from the above analysis.
ContributorsSiddiqui, Saquib Ahmad (Author) / Bliss, Daniel (Thesis advisor) / Chakrabarti, Chaitali (Committee member) / Ogras, Umit Y. (Committee member) / Jayasuriya, Suren (Committee member) / Arizona State University (Publisher)
Created2020