Advances in Functional Decomposition: Theory and Applications

Functional decomposition aims at finding efficient representations for Boolean functions. It is used in many applications, including multi-level logic synthesis, formal verification, and testing. This dissertation presents novel heuristic algorithms for functional decomposition. These algorithms take advantage of suitable representations of the Boolean functions in order to be efficient. The first two algorithms compute simple-disjoint and disjoint-support decompositions. They are based on representing the target function by a Reduced Ordered Binary Decision Diagram (BDD). Unlike other BDD-based algorithms, the presented ones can deal with larger target functions and produce more decompositions without requiring expensive manipulations of the representation, particularly BDD reordering. The third algorithm also finds disjoint-support decompositions, but it is based on a technique which integrates circuit graph analysis and BDD-based decomposition. The combination of the two approaches results in an algorithm which is more robust than a purely BDD-based one, and that improves both the quality of the results and the running time. The fourth algorithm uses circuit graph analysis to obtain non-disjoint decompositions. We show that the problem of computing non-disjoint decompositions can be reduced to the problem of computing multiple-vertex dominators. We also prove that multiple-vertex dominators can be found in polynomial time. This result is important because there is no known polynomial time algorithm for computing all non-disjoint decompositions of a Boolean function. The fifth algorithm provides an efficient means to decompose a function at the circuit graph level, by using information derived from a BDD representation. This is done without the expensive circuit re-synthesis normally associated with BDD-based decomposition approaches. Finally we present two publications that resulted from the many detours we have taken along the winding path of our research

Design of event-driven automatic gain control and high-speed data path for multichannel optical receiver arrays

The internet has become the ubiquitous tool that has transformed the lives of all of us. New broadband applications in the field of entertainment, commerce, industry, healthcare and social interactions demand increasingly higher data rates and quality of the networks and ICT infrastructure. In addition, high definition video streaming and cloud services will continue to push the demand for bandwidth. These applications are reshaping the internet into a content-centric network. The challenge is to transform the telecom optical networks and data centers such that they can be scaled efficiently, at low cost. Furthermore, from both an environmental and economic perspective, this scaling should go hand in hand with reduced power consumption. This stems from the desire to reduce CO2 emission and to reduce network operating costs while offering the same service level as today. In the current architecture of the internet, end-users connect to the public network using the access network of an internet service provider (ISP). Today, this access network either reuses the legacy copper or coaxial network or uses passive optical network (PON) technologies, among which the PON is the most energy efficient and provides the highest data rates. Traffic from the access network is aggregated with Ethernet switches and routed to the core network through the provider edge routers, with broadband network gateways (BNGs) to regulate access and usage. These regional links are collectively called the metro network. Data centers connect to the core network using their own dedicated gateway router. The problem of increasing data rates, while reducing the economic and environmental impact, has attracted considerable attention. The research described in this work has been performed in the context of two projects part of the European Union Seventh Framework Programme (FP7), which both aim for higher data rates and tight integration while keeping power consumption low. Mirage targets data center applications while C3PO focuses on medium-reach networks, such as the metro network. Specifically, this research considers two aspects of the high-speed optical receivers used in the communication networks: increasing dynamic range of a linear receiver for multilevel modulation through automatic gain control (AGC) and integration of multiple channels on a single chip with a small area footprint. The data centers of today are high-density computing facilities that provide storage, processing and software as a service to the end-user. They are comprised of gateway routers, a local area network, servers and storage. All of this is organized in racks. The largest units contain over 100 000 servers. The major challenges regarding data centers are scalability and keeping up with increasing amounts of traffic while reducing power consumption (of the devices as well as the associated cooling) and keeping cost minimal. Presently, racks are primarily interconnected with active optical cables (AOCs) which employ signal rates up to 25 Gb/s per lane with non-return-to-zero (NRZ) modulation. A number of technological developments can be employed in AOCs of the future to provide terabit-capacity optical interconnects over longer distances. One such innovation is the use of multilevel modulation formats, which are more bandwidth-efficient than traditional NRZ modulation. Multilevel modulation requires a linear amplifier as front-end of the optical receiver. The greater part of this dissertation discusses the design and implementation of an AGC system for the data path of a linear transimpedance amplifier (TIA). The metro network is the intermediate regional network between the access and core network of the internet architecture, with link lengths up to 500 km. It is estimated that in the near future metro-traffic will increase massively. This growth is attributed mainly to increasing traffic from content delivery networks (CDNs) and data centers, which bypass the core network and directly connect to the metro network. Internet video growth is the major reason for traffic increase. This evolution demands increasingly higher data rates. Today, dense wavelength division multiplexing (DWDM) is widely recognized as being necessary to provide data capacity scalability for future optical networks, as it allows for much higher combined data rates over a single fiber. At the receiver, each wavelength of the demultiplexed incoming light is coupled to a photo diode in a photo diode array which is connected to a dedicated lane of a multichannel receiver. The high number of channels requires small physical channel spacing and tight integration of the diode array with the receiver. In addition, active cooling should be avoided, such that power consumption per receiver lane must be kept low in order not to exceed thermal operation limits. The second component of this work presents the development of an integrated four-channel receiver, targeting 4 × 25 Gb/s data rate, with low power consumption and small footprint to support tight integration with a p-i-n photo diode array with a 250 μm channel pitch. Chapter 1 discusses the impact of increasing data rates and the desire to reduce power consumption on the design of the optical receiver component, in wide metropolitan area networks as well as in short-reach point-to-point links in data centers. In addition, some aspects of integrated analog circuit design are highlighted: the design flow, transistor hand models, a software design tool. Also, an overview of the process technology is given. Chapter 2 provides essential optical receiver concepts, which are required to understand the remainder of the work. Fundamentals of feedback AGC systems are discussed in the first part of Chapter 3. A basic system model is presented in the continuous-time domain, in which the variable gain amplifier (VGA) constitutes the multistage datapath of a linear optical receiver. To enable reliable reception of multilevel modulation formats, the VGA requires controlled frequency response and in particular limited time-domain overshoot across the gain range. It is argued that this control is hard to achieve with fully analog building blocks. Therefore, an event-driven approach is proposed as an extension of the continuous-time system. Both the structural and behavioral aspects are discussed. The result is a system model of a quantized AGC loop, upon which the system-level design, presented in Chapter 4, is based. In turn, Chapter 5 discusses the detailed implementation of the various building blocks on the circuit level and presents experimental results that confirm the feasibility of the proposed approach. Chapter 6 discusses the design and implementation of a 4 × 25 Gb/s optical receiver array for NRZ modulation with a small area footprint. The focus lies on the input stages and techniques to extend bandwidth and dynamic range are presented. Measurement results for NRZ and optical duobinary (ODB) modulation are presented, as well as the influence of crosstalk on the performance. Finally, Chapter 7 provides an overview of the foremost conclusions of the presented research and includes suggestions for future research. Two appendices are included. Appendix A gives an overview of the general network theorem (GNT), which is used throughout this work and which has been implemented numerically. The results from Appendix B, the analysis of a two-stage opamp compensated with capacitance multipliers, were used to design a building block for the AGC system

MIXSyn: An Efficient Logic Synthesis Methodology for Mixed XOR-AND/OR Dominated Circuits

We present a new logic synthesis methodology, called MIXSyn, that produces area-efficient results for mixed XOR-AND/OR dominated logic functions. MIXSyn is a two step synthesis process. The first step is a hybrid logic optimization that enables selective and distinct optimization of AND/OR and XOR-intensive portions of the logic circuit. The second step is a library-free technology mapping that enhances design flexibility with a tractable computational cost. MIXSyn has been tested on a set of large MCNC benchmarks. Experimental results indicate that MIXSyn produces CMOS circuits with 18.0% and 9.2% fewer devices, on the average, with respect to state-of-art academic and commercial synthesis tools, respectively. MIXSyn is also capable to exploit the opportunity of novel XOR implementations offered by the use of double-gate ambipolar devices. Experimental results show that MIXSyn can reduce the number of ambipolar transistors by 20.9% and 15.3%, on the average, with respect to state-of-art academic and commercial synthesis tools, respectively

Advanced Interior Point Formulation for the Global Routing Problem

As the circuit size increases in modern electronics, the design process becomes more complicated. Even though the hardware design process is divided into multiple phases, many of the divided problems are still extremely time consuming to solve. One of these NP-hard problems is the routing problem. As electronics step into the deep submicron era, optimizing the routing becomes increasingly important. One of the methods to solve global routing is to formulate the problem as an integer programming (IP) problem. This formulation can then be relaxed into a linear programming problem and solved using interior point method. This thesis investigates two new approaches to optimize the speed of solving global routing using Karmarkar’s interior point method, as well as the effect of combining various optimizations with these new approaches. The first proposed approach is to utilize solution stability as the interior point loop converges, and attempt to remove solutions that have already stabilized. This approach reduces the problem size and allows subsequent interior point iterations to proceed faster. The second proposed approach is to solve the inner linear system (projection step) in interior point method in parallel. Experimental results show that for large routing problems, the performance of the solver is improved by the optimization approaches. The problem reduction stage allows for great speedup in the interior point iterations, without affecting the quality of the solution significantly. Furthermore, the timing required to solve inner linear system in the interior point method is improved by solving the problem in parallel. With these optimizations, solving the routing problem using the IP formation becomes increasingly more efficient. By solving an efficient parallel IP formation rather than a traditional sequential approach, more efficient optimal solutions which incorporate multiple conflicting objectives can be achieved

Decomposition tool targeting FPGA architectures

The growing interest in the field of logic synthesis targeting Field Programmable Gate Arrays (FPGA) and the active research carried out by a number of research groups in the area of functional decomposition is the prime motivation for this thesis. Logic synthesis has been an area of interest in many universities all over the world. The work involves the study and implementation of techniques and methods in logic synthesis. In this work, a logic synthesis tool has been developed implementing the aspects of general and complete Decomposition method based on functional decomposition techniques [4]. The tool is aimed at producing outputs faster and more efficient than the available software. C++ Standard template library is used to develop this tool. The output of this tool is designed to be compatible with the available vendor software. The tool has been tested on MCNC benchmarks and those created keeping in mind the industry requirements

Doctor of Philosophy

dissertationRecent breakthroughs in silicon photonics technology are enabling the integration of optical devices into silicon-based semiconductor processes. Photonics technology enables high-speed, high-bandwidth, and high-fidelity communications on the chip-scale-an important development in an increasingly communications-oriented semiconductor world. Significant developments in silicon photonic manufacturing and integration are also enabling investigations into applications beyond that of traditional telecom: sensing, filtering, signal processing, quantum technology-and even optical computing. In effect, we are now seeing a convergence of communications and computation, where the traditional roles of optics and microelectronics are becoming blurred. As the applications for opto-electronic integrated circuits (OEICs) are developed, and manufacturing capabilities expand, design support is necessary to fully exploit the potential of this optics technology. Such design support for moving beyond custom-design to automated synthesis and optimization is not well developed. Scalability requires abstractions, which in turn enables and requires the use of optimization algorithms and design methodology flows. Design automation represents an opportunity to take OEIC design to a larger scale, facilitating design-space exploration, and laying the foundation for current and future optical applications-thus fully realizing the potential of this technology. This dissertation proposes design automation for integrated optic system design. Using a buildingblock model for optical devices, we provide an EDA-inspired design flow and methodologies for optical design automation. Underlying these flows and methodologies are new supporting techniques in behavioral and physical synthesis, as well as device-resynthesis techniques for thermal-aware system integration. We also provide modeling for optical devices and determine optimization and constraint parameters that guide the automation techniques. Our techniques and methodologies are then applied to the design and optimization of optical circuits and devices. Experimental results are analyzed to evaluate their efficacy. We conclude with discussions on the contributions and limitations of the approaches in the context of optical design automation, and describe the tremendous opportunities for future research in design automation for integrated optics

Low Power Design Techniques for Digital Logic Circuits.

With the rapid increase in the density and the size of chips and systems, area and power dissipationbecome critical concern in Very Large Scale Integrated (VLSI) circuit design. Low powerdesign techniques are essential for today's VLSI industry. The history of symbolic logic and sometypical techniques for finite state machine (FSM) logic synthesis are reviewed.The state assignment is used to optimize area and power dissipation for FSMs. Two costfunctions, targeting area and power, are presented. The Genetic Algorithm (GA) is used to searchfor a good state assignment to minimize the cost functions. The algorithm has been implementedin C. The program can produce better results than NOVA, which is integrated into SIS by DCBerkeley, and other publications both in area and power tested by MCNC benchmarks.Flip-flops are the core components of FSMs. The reduction of power dissipation from flip-flopscan save power for digital systems significantly. Three new kinds of flip-flops, called differentialCMOS single edge-triggered flip-flop with clock gating, double edge-triggered and multiple valuedflip-flops employing multiple valued clocks, are proposed. All circuits are simulated using PSpice.Most researchers have focused on developing low-power techniques in AND/OR or NAND& NOR based circuits. The low power techniques for AND /XOR based circuits are still intheir early stage of development. To implement a complex function involving many inputs,a form of decomposition into smaller subfunctions is required such that the subfunctions fitinto the primitive elements to be used in the implementation. Best polarity based XOR gatedecomposition technique has been developed, which targets low power using Huffman algorithm.Compared to the published results, the proposed method shows considerable improvement inpower dissipation. Further, Boolean functions can be expressed by Fixed Polarity Reed-Muller(FPRM) forms. Based on polarity transformation, an algorithm is developed and implementedin C language which can find the best polarity for power and area optimization. Benchmarkexamples of up to 21 inputs run on a personal computer are given

Measurements, Models, Systems and Design

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