Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Quasi-random sequences and their discrepancies
SIAM Journal on Scientific Computing
Algorithm 659: Implementing Sobol's quasirandom sequence generator
ACM Transactions on Mathematical Software (TOMS)
Efficient algorithms for computing the L2-discrepancy
Mathematics of Computation
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
Journal of Complexity
Complexity and information
Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators
ACM Transactions on Mathematical Software (TOMS)
Remark on algorithm 659: Implementing Sobol's quasirandom sequence generator
ACM Transactions on Mathematical Software (TOMS)
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
The effective dimension and quasi-Monte Carlo integration
Journal of Complexity
Algorithm 823: Implementing scrambled digital sequences
ACM Transactions on Mathematical Software (TOMS)
Sufficient conditions for fast quasi-Monte Carlo convergence
Journal of Complexity
Why Are High-Dimensional Finance Problems Often of Low Effective Dimension?
SIAM Journal on Scientific Computing
Statistical timing analysis under spatial correlations
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Statistical Timing Analysis: From Basic Principles to State of the Art
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Low-Discrepancy Sequences and Global Function Fields with Many Rational Places
Finite Fields and Their Applications
Adjustment-based modeling for timing analysis under variability
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Adaptive sampling for efficient failure probability analysis of SRAM cells
Proceedings of the 2009 International Conference on Computer-Aided Design
Proceedings of the 47th Design Automation Conference
Practical Monte-Carlo based timing yield estimation of digital circuits
Proceedings of the Conference on Design, Automation and Test in Europe
Statistical static timing analysis using Markov chain Monte Carlo
Proceedings of the Conference on Design, Automation and Test in Europe
Correlation controlled sampling for efficient variability analysis of analog circuits
Proceedings of the Conference on Design, Automation and Test in Europe
Graph partition based path selection for testing of small delay defects
Proceedings of the 2010 Asia and South Pacific Design Automation Conference
Advanced variance reduction and sampling techniques for efficient statistical timing analysis
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Residue arithmetic for variation-tolerant design of multiply-add units
PATMOS'09 Proceedings of the 19th international conference on Integrated Circuit and System Design: power and Timing Modeling, Optimization and Simulation
A lower bound computation method for evaluation of statistical design techniques
Proceedings of the International Conference on Computer-Aided Design
Integration, the VLSI Journal
Hi-index | 0.00 |
The Monte-Carlo (MC) technique is a well-known solution for statistical analysis. In contrast to probabilistic (non-Monte Carlo) Statistical Static Timing Analysis (SSTA) techniques, which are typically derived from simple statistical or timing models, the MC-based SSTA technique encompasses complicated timing and process variation models. However, a precise analysis that involves a traditional MC-based technique requires many timing simulation runs (1000s). In this paper, the behavior of the critical delay of digital circuits is investigated by using a Legendre polynomial-based ANOVA decomposition. The analysis verifies that the variance of the critical delay is mainly due to the pairwise interactions among the Principal Components (PCs) of the process parameters. Based on this fact, recent progress on the MC-based SSTA, through Latin Hypercube Sampling (LHS), is also studied. It is shown that this technique is prone to inefficient critical delay variance and quantile estimating. Inspired by the decomposition observations, an efficient algorithm is proposed which produces optimally low L2-discrepancy Quasi-MC (QMC) samples which significantly improve the precision of critical delay statistical estimations, compared with that of the MC, LHS, and traditional QMC techniques.