Using Implications for Online Error Detection

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Using Implications for Online Error Detection

• Nuno Alves, Jennifer Dworak, R. Iris Bahar
• Division of Engineering
• Brown University
• Providence, RI 02912

Kundan Nepal Electrical Engineering
Dept. Bucknell University Lewisburg, PA 17837
NATW 2008
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Online error detection

• Purpose Detect transient faults that may occur
  in a circuit during operation
• Critical as circuits scale to smaller sizes
• Easy in memory logic
• In circuit logic not so easy

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Common online detection techniques

1. Stored pre-computed test vectors in hardware
2. Duplicating the computation of disjoint hardware
   elements and voting on the result
3. Use of check bits

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Our approach

• Find invariant relationships in a circuit
• Violations of these expected relationships can
  identify errors

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Error detection implementation
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Invariant relationships in circuits
These relationships are logic implications
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Error detection with implications
ERROR
n51 n81 will generate an error in checker
logic
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How we find implications
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We have implications. Now what?
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Why should we remove implications?

• With all implications we can generate checker
  logic for each implication.
• Inefficient!
• A circuit can contain thousands of implications
• generating separate checker logic for each
  implication could more than double circuit size.
• We want to detect only the most important
  implications.

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Removing redundant implications
n1
n2
n9
n12
n8
n13
n3
n10
n4
n5
n11
n6
n7
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Removing low coverage implications

• We only want implications that
• Detect many faults
• Identify hard-to-detect faults
• Cover faults not detected by other implications
• Finding these important implications requires
• fault analysis to determine the specific fault
  coverage for each implication

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Reducing the number of implications
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Covering faults with implications

• For each random input vector, and at each fault,
  the implications-based circuit operation can fall
  into the following 4 categories

Case 1 Case 2 Case 3 Case 4
Error Propagates To Output ? ? ? ?
An Implication is Violated ? ? ? ?
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Average distribution of the 4 scenarios
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How often do we detect errors?

• Case1/Case1Case4

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Implications with fixed HW budgets

• Given a fixed HW budget, by how much can we
  reduce the probability of an undetected error?

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Conclusions

• Practical online error detection alternative
  based on implication validation
• No modification of targeted logic
• Checker logic is added off the critical path and
  run in parallel rest of circuit.
• For several circuits, we can detect almost 90 of
  all errors that propagate to a primary output.
• With only a 10 area overhead, probability of an
  error being both observable and undetected is
  reduced to 11 on average