Combining Error-Correcting Codes and Decision Diagrams for the Design of Fault-Tolerant Logic

In modern logic circuits, fault-tolerance is increasingly important, since even atomic-scale imperfections can result in circuit failures as the size of the components is shrinking. Therefore, in addition to existing techniques for providing fault-tolerance to logic circuits, it is important to develop new techniques for detecting and correcting possible errors resulting from faults in the circuitry. Error-correcting codes are typically used in data transmission for error detection and correction. Their theory is far developed, and linear codes, in particular, have many useful properties and fast decoding algorithms. The existing fault-tolerance techniques utilizing error-correcting codes require less redundancy than other error detection and correction schemes, and such techniques are usually implemented using special decoding circuits. Decision diagrams are an efficient graphical representation for logic functions, which, depending on the technology, directly determine the complexity and layout of the circuit. Therefore, they are easy to implement. In this thesis, error-correcting codes are combined with decision diagrams to obtain a new method for providing fault-tolerance in logic circuits. The resulting method of designing fault-tolerant logic, namely error-correcting decision diagrams, introduces redundancy already to the representations of logic functions, and as a consequence no additional checker circuits are needed in the circuit layouts obtained with the new method. The purpose of the thesis is to introduce this original concept and provide fault-tolerance analysis for the obtained decision diagrams. The fault-tolerance analysis of error-correcting decision diagrams carried out in this thesis shows that the obtained robust diagrams have a significantly reduced probability for an incorrect output in comparison with non-redundant diagrams. However, such useful properties are not obtained without a cost, since adding redundancy also adds complexity, and consequently better error-correcting properties result in increased complexity in the circuit layout. /Kir1

An overview of decision table literature 1982-1995.

This report gives an overview of the literature on decision tables over the past 15 years. As much as possible, for each reference, an author supplied abstract, a number of keywords and a classification are provided. In some cases own comments are added. The purpose of these comments is to show where, how and why decision tables are used. The literature is classified according to application area, theoretical versus practical character, year of publication, country or origin (not necessarily country of publication) and the language of the document. After a description of the scope of the interview, classification results and the classification by topic are presented. The main body of the paper is the ordered list of publications with abstract, classification and comments.

Synthesis and Optimization of Reversible Circuits - A Survey

Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, post-synthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms --- search-based, cycle-based, transformation-based, and BDD-based --- as well as specific algorithms for reversible synthesis, both exact and heuristic. We conclude the survey by outlining key open challenges in synthesis of reversible and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table

Specification format and a verification method of fault-tolerant quantum circuits

© 2018 American Physical Society. Quantum computations are expressed in general as quantum circuits, which are specified by ordered lists of quantum gates. The resulting specifications are used during the optimization and execution of the expressed computations. However, the specification format makes it difficult to verify that optimized or executed computations still conform to the initial gate list specifications: showing the computational equivalence between two quantum circuits expressed by different lists of quantum gates is exponentially complex in the worst case. In order to solve this issue, this work presents a derivation of the specification format tailored specifically for fault-tolerant quantum circuits. The circuits are considered a form consisting entirely of single qubit initializations, cnot gates, and single qubit measurements (ICM form). This format allows, under certain assumptions, to efficiently verify optimized (or implemented) computations. Two verification methods based on checking stabilizer circuit structures are presented

The 1991 3rd NASA Symposium on VLSI Design

Papers from the symposium are presented from the following sessions: (1) featured presentations 1; (2) very large scale integration (VLSI) circuit design; (3) VLSI architecture 1; (4) featured presentations 2; (5) neural networks; (6) VLSI architectures 2; (7) featured presentations 3; (8) verification 1; (9) analog design; (10) verification 2; (11) design innovations 1; (12) asynchronous design; and (13) design innovations 2

Fault tolerance in reversible logic

In recent years reversible logic has offered a promising alternative to traditional logic circuits. Reversible logic introduces a mechanism which allows theoretically zero energy dissipation by eliminating the possibility of information loss. However, it is also desirable that all computation should ideally be done in a fault tolerant manner. To address this we propose techniques to achieve fault tolerance in reversible logic based on a passive hardware redundancy technique. We propose two new designs for a reversible majority voter circuit that can be used to implement fault masking. Comparisons to existing designs are presented in terms of cost metrics such as gate count, garbage outputs, constant inputs, and quantum cost. Comparative failure probability analysis of the proposed voter circuits is also provided. Simulation results of the voter circuit failure probabilities over different numbers of trials are also presented. Our approach can be used to determine the circuit failure probability by using the gate failure probabilities. The proposed methodology can provide useful information for future reversible gate fabrication and designing future fault tolerant reversible circuits

NASA Space Engineering Research Center for VLSI systems design

This annual review reports the center's activities and findings on very large scale integration (VLSI) systems design for 1990, including project status, financial support, publications, the NASA Space Engineering Research Center (SERC) Symposium on VLSI Design, research results, and outreach programs. Processor chips completed or under development are listed. Research results summarized include a design technique to harden complementary metal oxide semiconductors (CMOS) memory circuits against single event upset (SEU); improved circuit design procedures; and advances in computer aided design (CAD), communications, computer architectures, and reliability design. Also described is a high school teacher program that exposes teachers to the fundamentals of digital logic design

Formal Verification throughout the Development of Robust Systems

As transistors are becomming smaller and smaller, they become more susceptible to transient faults due to radiation. A system can be modified to handle these faults and prevent errors that are visible from outside. We present a formal method for equivalence checking to verify that this modification does not change the nominal behavior of the system. On the other hand, we contribute an algorithm to formally verify that a circuit is robust against transient faults under all possible input assignments and variability. If equivalence or robustness cannot be shown, a counterexample is generated

Design, Analysis and Test of Logic Circuits under Uncertainty.

Integrated circuits are increasingly susceptible to uncertainty caused by soft errors, inherently probabilistic devices, and manufacturing variability. As device technologies scale, these effects become detrimental to circuit reliability. In order to address this, we develop methods for analyzing, designing, and testing circuits subject to probabilistic effects. Our main contributions are: 1) a fast, soft-error rate (SER) analyzer that uses functional-simulation signatures to capture error effects, 2) novel design techniques that improve reliability using little area and performance overhead, 3) a matrix-based reliability-analysis framework that captures many types of probabilistic faults, and 4) test-generation/compaction methods aimed at probabilistic faults in logic circuits. SER analysis must account for the main error-masking mechanisms in ICs: logic, timing, and electrical masking. We relate logic masking to node testability of the circuit and utilize functional-simulation signatures, i.e., partial truth tables, to efficiently compute estability (signal probability and observability). To account for timing masking, we compute error-latching windows (ELWs) from timing analysis information. Electrical masking is incorporated into our estimates through derating factors for gate error probabilities. The SER of a circuit is computed by combining the effects of all three masking mechanisms within our SER analyzer called AnSER. Using AnSER, we develop several low-overhead techniques that increase reliability, including: 1) an SER-aware design method that uses redundancy already present within the circuit, 2) a technique that resynthesizes small logic windows to improve area and reliability, and 3) a post-placement gate-relocation technique that increases timing masking by decreasing ELWs. We develop the probabilistic transfer matrix (PTM) modeling framework to analyze effects beyond soft errors. PTMs are compressed into algebraic decision diagrams (ADDs) to improve computational efficiency. Several ADD algorithms are developed to extract reliability and error susceptibility information from PTMs representing circuits. We propose new algorithms for circuit testing under probabilistic faults, which require a reformulation of existing test techniques. For instance, a test vector may need to be repeated many times to detect a fault. Also, different vectors detect the same fault with different probabilities. We develop test generation methods that account for these differences, and integer linear programming (ILP) formulations to optimize test sets.Ph.D.Computer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/61584/1/smita_1.pd