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Hierarchical Cross-Entropy Optimization for Fast On-Chip Decap Budgeting

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5 Author(s)
Xueqian Zhao ; Dept. of Electr. & Comput. Eng., Michigan Technol. Univ., Houghton, MI, USA ; Yonghe Guo ; Xiaodao Chen ; Zhuo Feng
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Decoupling capacitor (decap) has been widely used to effectively reduce dynamic power supply noise. Traditional decap budgeting algorithms usually explore the sensitivity-based nonlinear optimizations or conjugate gradient (CG) methods, which can be prohibitively expensive for large-scale decap budgeting problems and cannot be easily parallelized. In this paper, we propose a hierarchical cross-entropy based optimization technique which is more efficient and parallel-friendly. Cross-entropy (CE) is an advanced optimization framework which explores the power of rare event probability theory and importance sampling. To achieve the high efficiency, a sensitivity-guided cross-entropy (SCE) algorithm is introduced which integrates CE with a partitioning-based sampling strategy to effectively reduce the solution space in solving the large-scale decap budgeting problems. Compared to improved CG method and conventional CE method, SCE with Latin hypercube sampling method (SCE-LHS) can provide 2× speedups, while achieving up to 25% improvement on power supply noise. To further improve decap optimization solution quality, SCE with sequential importance sampling (SCE-SIS) method is also studied and implemented. Compared to SCE-LHS, in similar runtime, SCE-SIS can lead to 16.8% further reduction on the total power supply noise.

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Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on  (Volume:30 ,  Issue: 11 )