Robust FPGA Resynthesis Based on Fault-Tolerant Boolean Matching

1. Robust FPGA Resynthesis Based on Fault-Tolerant Boolean Matching Yu Hu1, Zhe Feng1, Lei He1 and Rupak Majumdar2 1Electrical Engineering Dept., UCLA 2Computer Science Dept., UCLA Presented by Yu Hu Address comments to lhe@ee.ucla.edu

2. Outline • Background and Motivation • Preliminaries • Robust Resynthesis Algorithms • Experimental Results • Conclusion and Future Work

3. Background • Late CMOS scaling reduces device reliability • Single event upset (SEU) due to cosmic rays • Affects configuration SRAM cells in FPGAs • Permanent soft error rate (SER) • Need rewriting SRAM for recovery • Affects combinational circuits and FFs • Transient SER • Can be recovered in multiple clock cycles

4. Fault Tolerance Techniques for FPGAs

5. Fault Tolerance Techniques for FPGAs Our work Low-cost, complementary approach to existing techniques! [A. Djupdal and P. Haddow, Yield Enhancing Defect Tolerance Techniques for FPGAs, MAPLD 2006]

6. Stochastic Synthesis and Logic Masking • Stochastic synthesis assumes probabilistic logic values to model effect of random defects • Break the conventional Boolean view which assumes deterministic Boolean ‘0’ and ‘1’ values • Key to stochastic synthesis: Logic Masking Masked faults 0 1

7. Stochastic Synthesis and Logic Masking (cont.) • Stochastic Synthesisintelligently places logic masking. • Logic Masking reduces the probability of the propagation of random faults • Maximizes the stochastic yield • However, logic synthesis to maximize yield rate w/o explicit redundancy and testing has not been studied for fault tolerance! • Key questions • How much does logic masking affect robustness? • How and where to place logic masking?

8. How much Logic Masking Affect Robustness? Different synthesis leads to different logic masking. Stochastic synthesis maximizes logic masking! 18 synthesis solutions obtained by Berkeley ABC (for MCNC i10, LUT bit fault rate = 0.1%)

9. How and Where to Place Logic Masking?— Our Major Contributions • Propose a Robust FPGA resynthesis (ROSE) • Maximize the stochastic yield rate for FPGAs • No need to locate faults • Use the same synthesis for different chips of one FPGA application • Proposed a new PLB template for robustness • ROSE + Robust Template reduces fault rate by 25% with 1% fewer LUTs, and increases MTBF by 31% while preserving the logic depth • compared to Berkeley ABC

10. Outline • Background • Preliminaries • Robust Resynthesis • Experimental Results • Conclusion and Future Work

11. FPGA Synthesis Flow • Attempt to re-map a logic block by Boolean matching • Boolean matching can be used to handle both homogenous and heterogeneous PLBs

12. FPGA Synthesis Flow (cont.) • Multi-iterations of Boolean Matching-based Resynthesis (Source: Andrew Ling, University of Toronto, DAC'05)

13. Boolean Matching for Resynthesis 2-LUT f g 2-LUT 2-LUT 2-LUT ? 2-LUT • Formulate the sub-problem of resynthesis to Boolean matching (BM) • BM: Can function fbe implemented in circuit g ? • Resynthesis: Is there a configuration to gso that for all inputs to g, f is equivalent to g? • Existing algorithms: area/delay-optimal (Source: Andrew Ling, University of Toronto, DAC'05)

14. Outline • Background • Preliminaries • Robust Resynthesis • Problem Formulation • FTBM Algorithm • Robust PLB Template • Experimental Results • Conclusion and Future Work

15. Modeling of Faults • Model both faults in LUT configurations and the faults in intermediate wires as random variables, whose probabilities are given as inputs of our problem.

16. ROSE: Robust Resynthesis w/ FTBM • Boolean Matching • Inputs • PLB H and Boolean function F • Fault rates for the inputs and the SRAM bits of the PLB • Outputs • Either that F cannot be implemented by PLB H • Or the configuration of Hwhich minimizes the probability that the faults are observable in the output of the PLB under all input vectors. • FTBM tasks breakdown: • Step 1: Find a Boolean matching solution • Step 2: Evaluation the stochastic fault rate of a solution • Fault-Tolerant Boolean Matching

17. FTBM Step1: SAT Encoding for FTBM Conjunctive Normal Form (CNF) • If implementable, multiple configurations might exist • The one with minimal fault rate is needed!

18. Stochastic SAT Deterministic SAT Deterministic SAT vs. SSAT FTBM Step2: Fault Rate Calculation Based on SSAT • Simulation-based fault rate calculation • Not scalable for multiple defects • SAT-based fault rate calculation • Intelligently modeling random defects

19. GUI Version 1 SSAT Encoding for Fault Rate Calculation Binary search is performed to find the maximal β Faults in intermediate wires Faults in LUT configurations

20. Boolean matching Example: SAT-Based FTBM g= !x1!x3+ !x2 PLB Template Boolean function

21. PLB Characteristic Function:G = G LUT1 ·G LUT2 · G LUT3 Example: SAT-Based FTBMStep1: CNFs for the PLB template G LUT = ( x1 + x2+ ¬L0 + z) ( x1 + x2+ L0 + ¬ z) ( x1 + ¬x2+ ¬L1 + z) ( x1 + ¬x2+ L1 + ¬ z) (¬x1 + x2+ ¬L2 + z) (¬x1 + x2+ L2 + ¬ z) (¬x1 + ¬x2+ ¬L3 + z) (¬x1 + ¬x2+ L3 + ¬ z)

22. SAT Instance: G expand = G[X/000, f/1, z/z0] · G[X/001, f/1, z/z1] G[X/010, f/1, z/z2] · G[X/011, f/0, z/z3] G[X/100, f/1, z/z4] · G[X/101, f/1, z/z5] G[X/110, f/0, z/z6] · G[X/111, f/0, z/z7] Example: SAT-Based FTBMStep2: Replication based on Truth Table G = G LUT1 ·G LUT2· G LUT3 Replication

23. SAT Instance: G expand = G[X/000, f/1, z/z0] · G[X/001, f/1, z/z1] G[X/010, f/1, z/z2] · G[X/011, f/0, z/z3] G[X/100, f/1, z/z4] · G[X/101, f/1, z/z5] G[X/110, f/0, z/z6] · G[X/111, f/0, z/z7] Example: SAT-Based FTBMStep3: SAT Solving and Mapping Returned SAT assignments: L1(00) = 0, L1(01)=0, L1(10)=0, L1(11)=1, … SAT!

24. ¬ (L1(00) = 0, L1(01)=0, L1(10)=0, L1(11)=1, …) /* Complement of previous SAT assignments */ Augmented SAT Instance: G expand = G[X/000, f/1, z/z0] · G[X/001, f/1, z/z1] G[X/010, f/1, z/z2] · G[X/011, f/0, z/z3] G[X/100, f/1, z/z4] · G[X/101, f/1, z/z5] G[X/110, f/0, z/z6] · G[X/111, f/0, z/z7] New Configuration Previous Configuration Example: SAT-Based FTBMStep4: Exploring More SAT Solutions Fault rate = 0.2 Fault rate = 0.3

25. PLB Templates for SAT-based Resynthesis • Area efficient templates [A. Ling, DAC’05] • Proposed robust template w/ path-reconvergence • Can be configured by existing FPGAs

26. Templates for SAT-based Resynthesis (cont.) • Robust PLB template introduces more potential of don’t-cares • ROSE maximizes don’t-cares iteratively at each template output Observability don’t-care Satisfiability don’t-care

27. Outline • Background • Preliminaries • Robust Resynthesis • Experimental Results • Conclusion and Future Work

28. Experimental Settings • Implementation in OAGear • SAT-BM uses miniSAT2.0 • QUIP benchmarks are tested • Are first mapped with 4-LUTs by Berkeley ABC • Resynthesis settings • One traversal is performed • Blocks with up to 10 inputs are considered • The fault rate of the chip is calculated by Monte Carlo simulation with 20K random vectors assuming the single fault • Results are verified by ABC equivalency checkers

29. >30% fault rate reduction! Full-chip Fault Rate by Monte Carlo Simulation • Fault rate is the percentage of input vectors that cause observable output errors assuming the single fault.

30. Area (LUT#) ABC vs. ROSE/A vs. ROSE/R: 1: 0.9 : 0.99

31. 31% MTBF increase! Estimation of Mean Time Between Failure • SER modeling: [Mukherjee, HPCA, 2005] • Assume max-size FPGA: 330,000 LUTs

32. Outline • Background • Preliminaries • Robust Resynthesis • Experimental Results • Conclusion and Future Work

33. Conclusions and Future Work • Developed ROSE and a robust template. • ROSE is an orthogonal approach compared to existing fault-tolerant technique. • Virtually no overhead on power, delay and area • In the future, we will consider • Multiple correlated faults, • Alternative algorithms, • Extension to standard cell-based circuits, • Impacts on testability.

34. Robust FPGA Resynthesis Based on Fault-Tolerant Boolean Matching Yu Hu, Zhe Feng, Rupak Majumdar and Lei He University of California, Los Angeles