Digital Signal Processing and Machine Learning System Design using Stochastic Logic

Abstract

Digital signal processing (DSP) and machine learning systems play a crucial role in the fields of big data and artificial intelligence. The hardware design of these systems is extremely critical to meet stringent application requirements such as extremely small size, low power consumption, and high reliability. Following the path of Moore's Law, the density and performance of hardware systems are dramatically improved at an exponential pace. The increase in the number of transistors on a chip, which plays the main role in improvement in the density of circuit design, causes rapid increase in circuit complexity. Therefore, low area consumption is one of the key challenges for IC design, especially for portable devices. Another important challenge for hardware design is reliability. A chip fabricated using nanoscale complementary metal-oxide-semiconductor (CMOS) technologies will be prone to errors caused by fluctuations in threshold voltage, supply voltage, doping levels, aging, timing errors and soft errors. Design of nanoscale failure-resistant systems is currently of significant interest, especially as the technology scales below 10 nm. Stochastic Computing (SC) is a novel approach to address these challenges in system and circuit design. This dissertation considers the design of digital signal processing and machine learning systems in stochastic logic. The stochastic implementations of finite impulse response (FIR) and infinite impulse response (IIR) filters based on various lattice structures are presented. The implementations of complex functions such as trigonometric, exponential, and sigmoid, are derived based on truncated versions of their Maclaurin series expansions. We also present stochastic computation of polynomials using stochastic subtractors and factorization. The machine learning systems including artificial neural network (ANN) and support vector machine (SVM) in stochastic logic are also presented. First, we propose novel implementations for linear-phase FIR filters in stochastic logic. The proposed design is based on lattice structures. Compared to direct-form linear-phase FIR filters, linear-phase lattice filters require twice the number of multipliers but the same number of adders. The hardware complexities of stochastic implementations of linear-phase FIR filters for direct-form and lattice structures are comparable. We propose stochastic implementation of IIR filters using lattice structures where the states are orthogonal and uncorrelated. We present stochastic IIR filters using basic, normalized and modified lattice structures. Simulation results demonstrate high signal-to-error ratio and fault tolerance in these structures. Furthermore, hardware synthesis results show that these filter structures require lower hardware area and power compared to two's complement realizations. Second, We present stochastic logic implementations of complex arithmetic functions based on truncated versions of their Maclaurin series expansions. It is shown that a polynomial can be implemented using multiple levels of NAND gates based on Horner's rule, if the coefficients are alternately positive and negative and their magnitudes are monotonically decreasing. Truncated Maclaurin series expansions of arithmetic functions are used to generate polynomials which satisfy these constraints. The input and output in these functions are represented by unipolar representation. For a polynomial that does not satisfy these constraints, it still can be implemented based on Horner's rule if each factor of the polynomial satisfies these constraints. format conversion is proposed for arithmetic functions with input and output represented in different formats, such as $\text{cos}\,\pi x$ given $x\in[0,1]$ and $\text{sigmoid(x)}$ given $x\in[-1,1]$. Polynomials are transformed to equivalent forms that naturally exploit format conversions. The proposed stochastic logic circuits outperform the well-known Bernstein polynomial based and finite-state-machine (FSM) based implementations. Furthermore, the hardware complexity and the critical path of the proposed implementations are less than the Bernstein polynomial based and FSM based implementations for most cases. Third, we address subtraction and polynomial computations using unipolar stochastic logic. It is shown that stochastic computation of polynomials can be implemented by using a stochastic subtractor and factorization. Two approaches are proposed to compute subtraction in stochastic unipolar representation. In the first approach, the subtraction operation is approximated by cascading multi-levels of OR and AND gates. The accuracy of the approximation is improved with the increase in the number of stages. In the second approach, the stochastic subtraction is implemented using a multiplexer and a stochastic divider. We propose stochastic computation of polynomials using factorization. Stochastic implementations of first-order and second-order factors are presented for different locations of polynomial roots. From experimental results, it is shown that the proposed stochastic logic circuits require less hardware complexity than the previous stochastic polynomial implementation using Bernstein polynomials. Finally, this thesis presents novel architectures for machine learning based classifiers using stochastic logic. Three types of classifiers are considered. These include: linear support vector machine (SVM), artificial neural network (ANN) and radial basis function (RBF) SVM. These architectures are validated using seizure prediction from electroencephalogram (EEG) as an application example. To improve the accuracy of proposed stochastic classifiers, an approach of data-oriented linear transform for input data is proposed for EEG signal classification using linear SVM classifiers. Simulation results in terms of the classification accuracy are presented for the proposed stochastic computing and the traditional binary implementations based datasets from two patients. It is shown that accuracies of the proposed stochastic linear SVM are improved by 3.88\% and 85.49\% for datasets from patient-1 and patient-2, respectively, by using the proposed linear-transform for input data. Compared to conventional binary implementation, the accuracy of the proposed stochastic ANN is improved by 5.89\% for the datasets from patient-1. For patient-2, the accuracy of the proposed stochastic ANN is improved by 7.49\% by using the proposed linear-transform for input data. Additionally, compared to the traditional binary linear SVM and ANN, the hardware complexity, power consumption and critical path of the proposed stochastic implementations are reduced significantly.