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A mesh check-sum ABFT scheme for stream ciphers

INTERNATIONAL JOURNAL OF COMMUNICATION NETWORKS AND DISTRIBUTED SYSTEMS 2009年第4期3卷 285-300页

作者： Zhang, Chang N. Liu, Xiao Wei Univ Regina TRLabs Dept Comp Sci Regina SK S4S 0A2 Canada

To enhance the security and reliability of the widely-used stream ciphers, a novel mesh check-sum ABFT scheme for stream ciphers is developed. By utilising the ready-made arithmetic unit in stream ciphers, single and multiple errors can be detected and corrected in a cheap way. To meet different requirements in practical applications, 4-D mesh check-sum ABFT scheme is proposed which can be applied to RC4 or other stream ciphers. The 2-D mesh check-sum ABFT scheme is able to detect and correct single error with high efficiency. The 4-D mesh check-sum ABFT scheme is capable of correcting up to three errors located randomly in an N-element matrix with acceptable computation and bandwidth overhead. The workload can be remarkably reduced when most communications are error-free. Our scheme also provides one-to-one mapping between index and check-sum, so that error can be located and recovered by easier logic and simpler operation.

关键词： stream cipher algorithm-based fault tolerance error detection error correction RC4 parity check sum arithmetic unit matrix computation exclusive or

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fault tolerance design in JPEG 2000 image compression system

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IEEE TRANSACTIONS ON DEPENDABLE AND SECURE COMPUTING 2005年第1期2卷 57-75页

作者： Nguyen, C Redinbo, GR Univ Calif Davis Dept Elect & Comp Engn Davis CA 95616 USA

The JPEG 2000 image compression standard is designed for a broad range of data compression applications. The new standard is based on wavelet technology and layered coding in order to provide a rich feature compressed image stream. The implementations of the JPEG 2000 codec are susceptible to computer-induced soft errors. One situation requiring fault tolerance is remote-sensing satellites, where high energy, particles and radiation produce single event upsets corrupting the highly susceptible data compression operations. This paper develops fault tolerance error-detecting capabilities for the major subsysyems that constitute a JPEG 2000 standard. The nature of the subsystem dictates the realistic fault model where some parts have numerical error impacts whereas others are properly modeled using bit-level variables. The critical operations of subunits such as Discrete Wavelet Transform (DWT) and quantization are protected against numerical errors. Concurrent error detection techniques are applied to accommodate the data type and numerical operations in each processing unit. On the other hand, the Embedded Block Coding with Optimal Truncation (EBCOT) system and the bitstream formation unit are protected against soft-error effects using binary decision variables and cyclic redundancy check (CRC) parity values, respectively. The techniques achieve excellent error-detecting capability at only a slight increase in complexity. The design strategies have been tested using Matlab programs and simulation results are presented.

关键词： fault-tolerant source coding soft errors JPEG 2000 standard data compression Discrete Wavelet Transform (DWT) algorithm-based fault tolerance error control codes Huffman coding error-checking concurrent error detection hardware reliability weighted sum parity

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An efficient algorithm-based fault tolerance design using the weighted data-check relationship

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IEEE TRANSACTIONS ON COMPUTERS 2001年第4期50卷 371-383页

作者： Youn, HY Oh, CG Choo, H Chung, JW Lee, D Sungkyunkwan Univ Sch Elect & Comp Engn Suwon 440746 South Korea Nsyst Commun San Diego CA 92127 USA Informat & Commun Uni Sch Engn Taejon South Korea

VLSI-based processor arrays have been widely used for computation intensive applications such as matrix and graph algorithms. algorithm-based fault tolerance designs employing Various encoding/decoding schemes have been proposed for such systems to effectively tolerate operation time fault. In this paper, we propose an efficient algorithm-based fault tolerance design using the weighted data-check relationship, where the checks are obtained from the weighted data. The relationship is systematically defined as a new (n, k, N-w) Hamming checksum code, where n is the size of the code word, k is the number of information elements in the code word, and N-w is the number of weights employed, respectively. The proposed design with various weights is evaluated in terms of time and hardware overhead as well as overflow probability and round-off error. Two different schemes employing the (n, k, 2) and (n, k, 3) Hamming checksum code are illustrated using important matrix computations. Comparison with other schemes reveals that the (n, k, 3) Hamming checksum scheme is very efficient, while the hardware overhead is small.

关键词： algorithm-based fault tolerance Hamming correcting code matrix computations overflow round-off error VLSI processor array

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Concurrent error detection in wavelet lifting transforms

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IEEE TRANSACTIONS ON COMPUTERS 2004年第10期53卷 1291-1302页

作者： Redinbo, GR Nguyen, C Univ Calif Davis Dept Elect & Comp Engn Livermore CA 95616 USA

Wavelet transforms, central to multiresolution signal analysis and important in the JPEG2000 image compression standard, are quite susceptible to computer-induced errors because of their pipelined structure and multirate processing requirements. Such errors emanate from computer hardware, software bugs, or radiation effects from the surrounding environment. Implementations use lifting schemes, which employ update and prediction estimation stages, and can spread a single numerical error caused by failures to many output transform coefficients without any features to warn data users. This paper proposes an efficient method to detect the arithmetic errors using weighted sums of the wavelet coefficients at the output compared with an equivalent parity value derived from the input data. Two parity values may straddle a complete multistage transform or several values may be used, each pair covering a single stage. There is greater error-detecting capability at only a slight increase in complexity when parity pairs are interspersed between stages. With the parity weighting design scheme, a single error introduced at a lifting section can be detected. The parity computation operation is properly viewed as an inner product between weighting values and the data, motivating the use of dual space functionals related to the error gain matrices. The parity weighting values are generated by a combination of dual space functionals. An iterative procedure for evaluating the design of the parity weights has been incorporated in Matlab code and simulation results are presented.

关键词： wavelet transforms concurrent error detection weighted sum parity real number codes algorithm-based fault tolerance error gain matrices dual space functionals biorthogonality

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Protecting wavelet lifting transforms

Protecting wavelet lifting transforms

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10th IEEE Pacific Rim International Symposium on Dependable Computing (PRDC 2004)

作者： Redinbo, GR Nguyen, C Univ Calif Davis Dept Elect & Comp Engn Davis CA 95616 USA

ISBN: (纸本)0769520766

Wavelet transforms are the central to many applications in image processing and data compression. They have banks of multi-rate filters that are difficult to protect from. computer-induced numerical errors. An efficient algorithm-based fault tolerance approach is proposed for detecting arithmetic errors in the output data. Concurrent weighted parity values are designed to detect the effects of a single numerical error within the transform structure. The parity calculations use weighted sums of data, where the input parity weighting is related to the weighting used on the output data. Each parity computation is properly viewed as an inner product between weighting values and the data motivating the use of dual space functionals related to the error gain matrices that describe error propagations to the output. The parity weighting values are defined by a combination of dual space functionals. An iterative procedure for evaluating the design of the parity weights has been incorporated in Matlab code.

关键词： wavelet transforms concurrent error detection weighted sum parity real number codes algorithm-based fault tolerance error gain matrices dual space functionals bi-orthogonality

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Tests and tolerances for high-performance software-implemented fault detection

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IEEE TRANSACTIONS ON COMPUTERS 2003年第5期52卷 579-591页

作者： Turmon, M Granat, R Katz, DS Lou, JZ Jet Prop Lab Data Understanding Syst Grp Pasadena CA 91109 USA Jet Prop Lab Parallel Applicat Technol Grp Pasadena CA 91109 USA

We describe and test a software approach to fault detection in common numerical algorithms. Such result checking or algorithm-based fault tolerance (ABFT) methods may be used, for example, to overcome single-event upsets in computational hardware or to detect errors in complex, high-efficiency implementations of the algorithms. Following earlier work, we use checksum methods to validate results returned by a numerical subroutine operating subject to unpredictable errors in data. We consider common matrix and Fourier algorithms which return results satisfying a necessary condition having a linear form;the checksum tests compliance with this condition. We discuss the theory and practice of setting numerical tolerances to separate errors caused by a fault from those inherent in finite-precision floating-point calculations. We concentrate on comprehensively defining and evaluating tests having various accuracy/computational burden tradeoffs, and we emphasize average-case algorithm behavior rather than using worst-case upper bounds on error.

关键词： algorithm-based fault tolerance result checking error analysis aerospace parallel numerical algorithms

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An algorithm-based error detection scheme for the multigrid method

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IEEE TRANSACTIONS ON COMPUTERS 2003年第9期52卷 1089-1099页

作者： Mishra, A Banerjee, P Virginia Polytech Inst & State Univ Bradley Dept Elect & Comp Engn Blacksburg VA 24061 USA Northwestern Univ Dept Elect & Comp Engn Ctr Parallel & Distributed Comp Evanston IL 60208 USA

algorithm-based fault tolerance (ABFT) is a technique to provide system level error detection and correction on array processors as well as multiprocessors at a low cost. Since the early 80s the technique has been extensively applied to several linear algebraic algorithms, e.g., matrix multiplication, Gaussian elimination, QR factorization, and singular value decompositions, etc. An important class of problems in numerical linear algebra dealing with the iterative solution of linear algebraic equations arising due to the finite difference discretization or the finite element discretization of a partial differential equation, however, has been overlooked. The only exception is the recent application of algorithm based error detection (ABED) encodings to the successive overrelaxation algorithm for Laplace's equation [11]. In this paper, ABED is applied to a multigrid algorithm for the iterative solution of a Poisson equation in two dimensions. Invariants are created to implement checking in the relaxation, the restriction, and the interpolation operators. Modifications to invariants due to roundoff errors accumulated within the operators, which often lead to a situation known as false alarms, have been addressed by deriving the expressions for the roundoff errors in the algebraic processes in the operators and correcting the invariants accordingly, ABED encoded multigrid algorithm is shown to be insensitive to the size and the range of the input data besides providing excellent error coverage at a low latency for floating-point, integer, and memory errors.

关键词： algorithm-based fault tolerance multigrid method rounding error analysis parallel error detection partial differential equations

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Failure-detecting arithmetic convolutional codes and an iterative correcting strategy

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IEEE TRANSACTIONS ON COMPUTERS 2003年第11期52卷 1434-1442页

作者： Redinbo, GR Univ Calif Davis Dept Elect & Comp Engn Davis CA 95616 USA

Errors due to failures in data processing algorithms may be detected and even corrected by employing systematic convolutional codes defined over the fixed-point arithmetic structures supporting the computations. A new class of arithmetic convolutional codes using symbols from the finite ring associated with normal signed arithmetic is based on binary burst-correcting codes and a code's performance in the larger context exceeds that of an underlying basis code. When failures satisfy the usual guard band requirements for the binary code, error correction is possible using an iterative feedback decoder processing syndromes that are defined over the integers modulo a power of two. A class of high rate burst-correcting codes is discussed in more detail and their properties guarantee the detection of the onset of errors. The corrector also contains failure error-detecting capabilities.

关键词： algorithm-based fault tolerance convolutional codes over integers iterative decoding free modules fixed-point arithmetic burst-correcting codes syndrome decoding real number codes

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fault-tolerant computation in groups and semigroups: applications to automata, dynamic systems and Petri nets

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JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS 2002年第4-5期339卷 387-430页

作者： Hadjicostis, CN Verghese, GC Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA

The traditional approach to fault-tolerant computation has been via modular hardware redundancy. Although universal and simple, modular redundancy is inherently expensive and inefficient. By exploiting particular structural features of a computational architecture or an algorithm, arithmetic codes and recently developed algorithm-based fault tolerance (ABFT) techniques manage to introduce "analytical redundancy" and offer more efficient fault coverage at the cost of narrower applicability and harder design. In this paper, we extend a variety of results and constructive procedures that were developed in previous work for computations that take place in an abelian group to a more general setting that considers computations in semigroups. We demonstrate possible encodings for semigroup operations of interest and use our extension to design concurrent error detection and correction schemes for group and semigroup machines. The method provides insight regarding the role of decomposition in fault-tolerant algebraic machines and results in a general, hardware-independent characterization of concurrent error detection and correction in finite semiautomata. We also demonstrate that by extending this approach to other dynamic systems, with specific hardware implementations and failure modes, we can systematically obtain fault-tolerant architectures. More specifically, we apply these techniques to linear time-invariant dynamic systems and Petri net models of discrete event systems. (C) 2002 The Franklin Institute. Published by Elsevier Science Ltd. All rights reserved.

关键词： fault-tolerant computing group machines semigroup machines concurrent error detection concurrent error correction algorithm-based fault tolerance automata linear time-invariant dynamic systems Petri nets

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Combinatorial analysis of check set construction for algorithm-based fault tolerance systems

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JOURNAL OF ELECTRONIC TESTING-THEORY AND APPLICATIONS 1998年第3期12卷 255-260页

作者： Wang, DQ Zhao, LC Dalian Maritime Univ Dept Basic Sci Dalian 116026 Peoples R China

algorithm-based fault tolerance (ABFT) is a low-cost system-level concurrent error detection and fault location scheme. The design problem for an ABFT system is concerned with the construction of a check set for detecting errors or faults. In this paper, we analyze the construction of check sets from a combinatorial perspective, and propose a necessary and sufficient condition for the design of a check set that detects a given number of errors. We also propose a new bound for detecting three errors for algorithm-based fault tolerance systems.

关键词： algorithm-based fault tolerance check set combinatorial problem error detecting

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