Error-Correction

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Error-Correction CrosstalkAvoidance in DSM
Busses

• Ketan Patel and Igor Markov
• University of Michigan
• Electrical Engineering Computer Science
• 2003 ACM 1-58113-627-7/03/0004

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Outline

• Motivation
• Memoryless Codes
• Codes with memory
• Boundary shift codes

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Motivation

• DSM busses increasingly susceptible to noise
• Crosstalk
• Electromagnetic interference
• Power grid fluctuations
• Goal Avoid crosstalk provide
• error-correction

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Crosstalk Noise

• The severity of interference is correlated with
  the particular switching patterns on the bus.
• Bus value (t0) ? 0 1 1 0 0 0 1 1
• Bus value (t1) ? 1 1 0 1 1 0 1 0
• We call this an invalid transition
• A self-shielding code does not allow invalid
  transitions.

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Memoryless Model

• Vertices Bus Values
• Edges Valid Transitions
• Max clique?Optimal
• memoryless code
• distance d ? Detect d-1 errors
• can correct (d-1)/2 errors
• Place edges if
• Valid transition
• Distance large enough

3-bit codes example
(a)
(b)
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Codes with Memory

• Two graphs
• G1 crosstalk constraints
• G2 error-correction constraints
• For rate log2M code
• Vertices connected to M vertices in G1
• forming clique in G2

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Dependent Boundaries

• Dependent boundary boundary with transition
• 0 1 1 0 1 0 0 0
• Positions 1, 3, 4, 5
• No overlapping
• dependent boundaries?No invalid
• transition

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Boundary Shift Codes

• Start with error-correcting code
• Duplicate all bits (no odd dependent boundaries)
• Possibly puncture last bit position ? Code 1
• 1-bit circular right-shift ?Code 2
• Code 1 has no odd dependent boundaries
• Code 2 has no even dependent boundaries

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Boundary Shift Codes(example)

• Time Input Encoded Output
• 0 1010 110011000
• 1 0111 100111111
• Time Received
• 1 110111111
• 1-bit left-shift ?101111111
• Decode by majority vote ? 0111

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Advantages

• Advantages
• Practical encoder/decoder
• Scalable construction
• Systematic (unencoded wires)
• Drawbacks
• Encoding/decoding logic overhead
• Wire overhead

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Code Rates