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Layer Assignment Algorithm for RLC Crosstalk Minimization

Bin Liu, Yici Cai, Qiang Zhou, Xianlong Hong

Tsinghua University

23/4/18

Outline

Motivation and ObjectiveMotivation and Objective Crosstalk Cost Estimation Algorithm Description Experimental Results Conclusion

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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.

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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

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Objective

Minimize RLC crosstalk risk in layer assignment.

Minimize congestion in each layer. Cooperate with further crosstalk

mitigation techniques like shield insertion.

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Outline

Motivation and Objective Crosstalk Cost EstimationCrosstalk Cost Estimation Algorithm Description Experimental Results Conclusion

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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.

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Cost Function

Basically, on one GRC Edge

So the cost of crosstalk on one GRC is

1,

_ ,t

l l k

real noise N k l

_ _cost real noise noise budget

_noise budget L

1,

,t

k k l

Lcost N k l

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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

L

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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

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Outline

Motivation and Objective Crosstalk Cost Estimation Algorithm DescriptionAlgorithm Description Experimental Results Conclusion

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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

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Problem Formulation

Optimize Crosstalk cost Congestion

Congestion should be even at each layer Including the shields to be inserted

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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

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Algorithm FlowRepeatRepeat Ei is the unprocessed GRG-Edge with max W(e) RepeatRepeat

Nj is the unassigned net on Ei with max W(Nj)ForFor all layer pairs Assuming Nj is assigned to current layer pair Calculate global costEnd forEnd forAssign Nj to the layer pair with min global costUpdate the congestion of the layer pair

UntilUntil all nets that pass Ei has been assignedUntilUntil all GRG-Edges has been processed

Optimize the solution with simulated annealingOutput final solution

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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

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Outline

Motivation and Objective Crosstalk Cost Estimation Algorithm Description Experimental ResultsExperimental Results Conclusion

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Experimental Results

Industry instance, IBM benchmark Compared to a previous layer

assignment work in ASICON’03 Max coupling length of a net Congestion

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Experimental Results

max congestion ratio, ours/pre

SensRate

20% 30% 40% 50%

Gdc0.875/

0.80.875/

0.80.8/0.8

0.8/0.8

mibm01

0.55/0.45

0.5/0.45

0.45/0.45

0.5/0.45

mibm02

0.78/0.67

0.78/0.67

0.89/0.67

0.78/0.67

mibm07

0.64/0.56

0.62/0.56

0.60/0.56

0.62/0.56

mibm08

0.71/0.57

0.71/0.57

0.71/0.57

0.71/0.57

mibm10

0.57/0.57

0.63/0.57

0.6/0.57

0.6/0.57

max coupling length, ours/pre

SensRate

20% 30% 40% 50%

Gdc52/99

73/116

96/166

145/182

mibm01

74/123

74/137

83/224

125/240

mibm02

26/48

29/67

50/95

74/118

mibm07

32/54

62/67

78/91

129/213

mibm08

55/79

73/151

146/251

176/233

mibm10

91/135

130/171

155/233

216/340

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Outline

Motivation and Objective Crosstalk Cost Estimation Algorithm Description Experimental Results ConclusionConclusion

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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.

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Thanks.