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Accurate Prediction of Worst Case Eye Diagrams for Non-Linear Signaling Systems Aadithya V. Karthik*, Sayak Ray, Robert Brayton, and Jaijeet Roychowdhury EECS Dept., The University of California, Berkeley Mar 2014, TAU, Santa Cruz Aadithya V.

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Aadithya V. Karthik (aadithya@berkeley.edu) Mar 2014, TAU, Santa Cruz 1/17

Accurate Prediction of Worst Case Eye Diagrams for Non-Linear Signaling Systems

EECS Dept., The University of California, Berkeley

Mar 2014, TAU, Santa Cruz

Aadithya V. Karthik*, Sayak Ray, Robert Brayton, and Jaijeet Roychowdhury

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Aadithya V. Karthik (aadithya@berkeley.edu) Mar 2014, TAU, Santa Cruz 2/17

Overview of this talk

  • The Worst Case (WC) eye diagram problem

– Starting from the basics, i.e., what is an eye diagram?

  • Existing algorithms for WC eye estimation

– PDA, illustrated with an example

  • Where PDA fails

– Cannot handle general formulations of problem

  • A new algorithm for WC eye computation

– Illustrated with an example

  • Results

– 8b/10b encoder (PCI Express, USB, etc.) – Our technique is much less pessimistic than PDA

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SLIDE 3

Aadithya V. Karthik (aadithya@berkeley.edu) Mar 2014, TAU, Santa Cruz 3/17

What is an Eye Diagram (1/2)?

Analog Channel Bits Analogish “Bits” (delay, ISI, crosstalk, etc.)

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SLIDE 4

Aadithya V. Karthik (aadithya@berkeley.edu) Mar 2014, TAU, Santa Cruz 4/17

What is an Eye Diagram (2/2)?

Overlay sections between dashed vertical lines

Eye Eye WC Eye

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Aadithya V. Karthik (aadithya@berkeley.edu) Mar 2014, TAU, Santa Cruz 5/17

The Worst Case Eye Problem

Analog (LTI) Channel

Bit sequence Output eye

Digital System Problem: Compute worst-case eye

Arbitrary Correlated

  • Pure analog → PDA
  • Analog + Digital

– Non-Linear System – Correlated bits – PDA too pessimistic – Our new algorithm!

PDA

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SLIDE 6

Aadithya V. Karthik (aadithya@berkeley.edu) Mar 2014, TAU, Santa Cruz 6/17

Peak Distortion Analysis (PDA)

  • Assume channel is LTI
  • Key idea: WC Eye = 2 Optimization Problems

WC1 WC0

LTI Channel Linear combination of the bits! Correlated bits: PDA fails! Need mutually independent bits [0, 1, 0, 1, 1]

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SLIDE 7

Aadithya V. Karthik (aadithya@berkeley.edu) Mar 2014, TAU, Santa Cruz 7/17

FSMs for Modeling Correlated Bits

  • Finite number of states
  • Arcs denoting state transitions

– Each arc has an output bit

Analog (LTI) Channel

Bit sequence

Digital System

Correlated

FSM

For example, this FSM can never produce the sequence [0, 1, 1] Arbitrary digital logic, arbitrary bit correlations

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SLIDE 8

Aadithya V. Karthik (aadithya@berkeley.edu) Mar 2014, TAU, Santa Cruz 8/17

Algorithm for Correlated WC Eye

Key idea: Best partial sum ending in state Si

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SLIDE 9

Aadithya V. Karthik (aadithya@berkeley.edu) Mar 2014, TAU, Santa Cruz 9/17

Algorithm for Correlated WC Eye

Key idea: Best partial sum ending in state Si

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SLIDE 10

Aadithya V. Karthik (aadithya@berkeley.edu) Mar 2014, TAU, Santa Cruz 10/17

Algorithm for Correlated WC Eye

Key idea: Best partial sum ending in state Si

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SLIDE 11

Aadithya V. Karthik (aadithya@berkeley.edu) Mar 2014, TAU, Santa Cruz 11/17

Algorithm for Correlated WC Eye

Key idea: Best partial sum ending in state Si

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SLIDE 12

Aadithya V. Karthik (aadithya@berkeley.edu) Mar 2014, TAU, Santa Cruz 12/17

Algorithm for Correlated WC Eye

Key idea: Best partial sum ending in state Si

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SLIDE 13

Aadithya V. Karthik (aadithya@berkeley.edu) Mar 2014, TAU, Santa Cruz 13/17

Algorithm for Correlated WC Eye

Key idea: Best partial sum ending in state Si Compare to PDA, which pessimistically predicts 0.5 Dynamic programming

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SLIDE 14

Aadithya V. Karthik (aadithya@berkeley.edu) Mar 2014, TAU, Santa Cruz 14/17

Results: 8b/10b Encoder (1/2)

  • 8b/10b Encoder + LTI Channel

8b/10b Encoder

8b parallel

LTI Channel

10b serial

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SLIDE 15

Aadithya V. Karthik (aadithya@berkeley.edu) Mar 2014, TAU, Santa Cruz 15/17

Results: 8b/10b Encoder (2/2)

  • 8b/10b Encoder + LTI Channel

PDA Ours

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SLIDE 16

Aadithya V. Karthik (aadithya@berkeley.edu) Mar 2014, TAU, Santa Cruz 16/17

Summary

  • WC eye computation is important
  • Traditional PDA cannot handle bit correlations
  • Our new technique can
  • Key ideas behind our technique

– Model bit correlations as FSMs – Reduce WC eye computation to an optimization problem – Use dynamic programming to solve the above efficiently

  • Results

– (7, 4) Hamming code – 8b/10b Encoder

  • Future work

– Deterministic worst case → Probabilistic distributions

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SLIDE 17

Aadithya V. Karthik (aadithya@berkeley.edu) Mar 2014, TAU, Santa Cruz 17/17

Questions