Matrix analysis
A Linear Algebraic Model of Algorithm-Based Fault Tolerance
IEEE Transactions on Computers
Error-control coding for computer systems
Error-control coding for computer systems
Real-Number Codes for Fault-Tolerant Matrix Operations on Processor Arrays
IEEE Transactions on Computers
Algorithm-Based Fault Detection for Signal Processing Applications
IEEE Transactions on Computers
Mantissa-Preserving Operations and Robust Algorithm-Based Fault Tolerance for Matrix Computations
IEEE Transactions on Computers
Discrete-time signal processing (2nd ed.)
Discrete-time signal processing (2nd ed.)
The Design of Fault-Tolerant Linear Digital State Variable Systems: Theory and Techniques
IEEE Transactions on Computers
Locating and correcting errors in images
ICIP '97 Proceedings of the 1997 International Conference on Image Processing (ICIP '97) 3-Volume Set-Volume 1 - Volume 1
Algorithm-Based Fault Tolerance for Matrix Operations
IEEE Transactions on Computers
Determination of the Number of Errors in DFT Codes Subject to Low-Level Quantization Noise
IEEE Transactions on Signal Processing
Deterministic and iterative solutions to subset selection problems
IEEE Transactions on Signal Processing
Concurrent test for digital linear systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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This paper analyzes the effects of roundoff noise on our ability to nonconcurrently detect and identify transient faults that corrupt state variables during the operation of a fault-tolerant discrete-time linear time-invariant (LTI) dynamic system. Our analysis leads to two decoding algorithms, i.e., one based on the Peterson-Gorenstein-Zierler algorithm and the other based on singular-value decomposition techniques. We analytically obtain bounds on the roundoff noise level (equivalently, the precision) at which both algorithms can guarantee the correct determination of the number of errors. Our simulations verify our analysis and suggest that our bounds can be very tight for certain choices of design parameters. The developments in this paper can be used to provide guidance about the design of fault-tolerant systems and have immediate implications for digital implementations of LTI dynamic systems (e.g., digital filters) because such implementations unavoidably have to deal with finite-precision effects.