Design and FPGA Implementation of CORDIC-based 8-point 1D DCT Processor

CORDIC or CO-ordinate Rotation DIgital Computer is a fast, simple, efficient and powerful algorithm used for diverse Digital Signal Processing applications. Primarily developed for real-time airborne computations, it uses a unique computing technique which is especially suitable for solving the trigonometric relationships involved in plane co-ordinate rotation and conversion from rectangular to polar form. It comprises a special serial arithmetic unit having three shift registers, three adders/subtractors, Look-Up table and special interconnections. Using a prescribed sequence of conditional additions or subtractions the CORDIC arithmetic unit can be controlled to solve either of the following equations: Y’=K (Ycos λ+ Xsin λ) X’=K (Xcos λ - Ysin λ); where K is a constant In this project: • A CORDIC-based processor for sine/cosine calculation was designed using VHDL programming in Xilinx ISE 10.1. The CORDIC module was tested for its functionality and correctness by test-bench analysis. Subsequently, FPGA implementation of the CORDIC core followed by ChipScopePro analysis of the output logic waveforms was performed. • Using this CORDIC core a DCT processor was designed to calculate the 8-point 1D DCT. The functionality and operational correctness of this processor was tested, first on the test-bench and then via ChipScopePro analysis, post FPGA implementation. The output obtained in both the cases was compared with the actual values to test for consistency and the percentage of accuracy was established. Power consumption and FPGA resource utilization were observed. The results obtained were discussed

Trustworthy data from untrusted databases

Increasingly, data are subjected to environments which can result in invalid (malicious or inadvertent) modifications to the data. For example, when we host the database on a third party server, or when there is a threat of insider attack or hacker attack. Ensuring the trustworthiness of data retrieved from a database is of utmost importance to users. In this dissertation, we address the question of whether a data owner can be assured that the data retrieved from an untrusted server are trustworthy. In particular, we reduce the level of trust necessary in order to establish the trustworthiness of data. Earlier work in this domain is limited to situations where there are no updates to the database, or all updates are authorized and vetted by a central trusted entity. This is an unreasonable assumption for a truly dynamic database, as would be expected in many business applications, where multiple users can access (read or write) the data without being vetted by a central server. The legitimacy of data stored in a database is defined by the faithful execution of only valid (authorized) operations. Decades of database research has resulted in solutions that ensure the integrity and consistency of data through principles such as transactions, concurrency, ACID properties, and access control rules. These solutions have been developed under the assumption that the threats arise due to failures (computer crashes, disk failures, etc), limitations of hardware, and the need to enforce access control rules. However, the semantics of these principles assumes complete trust on the database server. Considering the lack of trust that arises due to the untrusted environments that databases are subjected to, we need mechanisms to ensure that the database operations are executed following these principles. In this dissertation, we revisit some of these principles to understand what we should expect when a transaction execution follows those principles. We propose mechanisms to verify that the principles were indeed followed by the untrusted server while executing the transactions

Regularity estimates for some free boundary problems of obstacle-type

We study regularity estimates for solutions to implicit constraint obstacle problems and penalized boundary obstacle problems. We first prove regularity estimates for the solution and the free boundary in the classical stochastic impulse control problem. We show that the free boundary partial {u < Mu}, where Mu is the implicit constraint obstacle, can be decomposed into a union of regular points, singular points, and degenerate points with corresponding regularity and measure theoretic estimates. We then turn to generalizing our analysis to the fully nonlinear problem with obstacles admitting a general modulus of semi-convexity omega(r). We prove that solutions to the fully nonlinear stochastic impulse control problem are C^{omega(r)} up to C^{1,1}. Finally we turn our attention to study both nonuniform and uniform estimates for the penalized boundary obstacle problem, Delta^{1/2}u^{epsilon} =beta_{epsilon} (u^{epsilon}). We obtain sharp estimates for the solution in both the nonuniform and uniform theory.Mathematic