Layer Assignment Algorithm for RLC Crosstalk Minimization

1. Layer Assignment Algorithm for RLC Crosstalk Minimization Bin Liu, Yici Cai, Qiang Zhou, Xianlong Hong Tsinghua University

2. Outline • Motivation and Objective • Crosstalk Cost Estimation • Algorithm Description • Experimental Results • Conclusion

3. Motivations • Crosstalk is becoming a vital factor in high performance designs. • Crosstalk consideration in early design stages is necessary. • Appropriate method to evaluate the crosstalk cost is needed for early crosstalk avoidance and mitigation.

4. Motivations • Layer assignment is an ideal step to address crosstalk. • Global routing: flexible but inaccurate • Detailed routing: accurate but lacks flexibility • As an intermediate stage, layer assignment combines accuracy and flexibility

5. Objective • Minimize RLC crosstalk risk in layer assignment. • Minimize congestion in each layer. • Cooperate with further crosstalk mitigation techniques like shield insertion.

6. Outline • Motivation and Objective • Crosstalk Cost Estimation • Algorithm Description • Experimental Results • Conclusion

8. Noise Budgeting • Assumption：Noises on each segment of a wire are independent on each other. • Given the noise constraint at a sink, we can distribute the noise onto each segment along the net according to segment length.

9. Cost Function • Basically, on one GRC Edge • So the cost of crosstalk on one GRC is

10. Further Explanation • From another perspective: • The same noise voltage on longer nets is more dangerous, the severity is proportional to the length • Severity is inversely proportional to the constraint • So, we use as a weight factor of noise

11. Noise Calculation • Various noise models with different considerations can be used. • Capacitive and Inductive • Statistically, the noise voltage is approximately proportional to the congestion of sensitive nets

12. Outline • Motivation and Objective • Crosstalk Cost Estimation • Algorithm Description • Experimental Results • Conclusion

13. Problem Formulation • Given: • Number of layers • The GRC’s that a net passes • Noise constraint at each sink • Sensitive matrix • Routing resources on each layer • Output: • Layer pair for each net

14. Problem Formulation • Optimize • Crosstalk cost • Congestion • Congestion should be even at each layer • Including the shields to be inserted

15. Algorithm Flow • 2-phase Algorithm • Initial solution • Assign the nets according to the weight • Among all possible assignment, the least-cost solution is adopted • Optimize using simulated annealing

16. Algorithm Flow Repeat Ei is the unprocessed GRG-Edge with max W(e) Repeat Nj is the unassigned net on Ei with max W(Nj) For all layer pairs Assuming Nj is assigned to current layer pair Calculate global cost End for Assign Nj to the layer pair with min global cost Update the congestion of the layer pair Until all nets that pass Ei has been assigned Until all GRG-Edges has been processed Optimize the solution with simulated annealing Output final solution

17. Strategies • Areas with larger congestion should take priority • Nets with higher sensitive rate should take priority • Nets with lower noise tolerance should take priority • Longer nets should take priority

18. Outline • Motivation and Objective • Crosstalk Cost Estimation • Algorithm Description • Experimental Results • Conclusion

19. Experimental Results • Industry instance, IBM benchmark • Compared to a previous layer assignment work in ASICON’03 • Max coupling length of a net • Congestion

20. Experimental Results

21. Outline • Motivation and Objective • Crosstalk Cost Estimation • Algorithm Description • Experimental Results • Conclusion

22. Conclusion • Crosstalk control in layer assignment is necessary and effective. • With consideration of net length, we could prevent longer nets suffer too much noise. • Successive work could combine layer assignment with track assignment, wire sizing/spacing to achieve better results. This work is on going.

23. Thanks.