Accurate Prediction of Worst Case Eye Diagrams for Non-Linear

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1 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. Karthik ([email protected]) Mar 2014, TAU, Santa Cruz 1/17

2 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 Aadithya V. Karthik ([email protected]) Mar 2014, TAU, Santa Cruz 2/17

3 What is an Eye Diagram (1/2)? Bits Analog Channel Analogish Bits (delay, ISI, crosstalk, etc.) Aadithya V. Karthik ([email protected]) Mar 2014, TAU, Santa Cruz 3/17

4 What is an Eye Diagram (2/2)? Eye Overlay sections between dashed vertical lines WC Eye Eye Aadithya V. Karthik ([email protected]) Mar 2014, TAU, Santa Cruz 4/17

5 The Worst Case Eye Problem Correlated Arbitrary Bit sequence Analog (LTI) Digital System Channel PDA Output eye Pure analog PDA Analog + Digital Non-Linear System Correlated bits PDA too pessimistic Problem: Compute Our new algorithm! worst-case eye Aadithya V. Karthik ([email protected]) Mar 2014, TAU, Santa Cruz 5/17

6 Peak Distortion Analysis (PDA) Assume channel is LTI Key idea: WC Eye = 2 Optimization Problems LTI Channel WC1 WC0 Linear combination of the bits! Need mutually independent bits [0, 1, 0, 1, 1] Correlated bits: PDA fails! Aadithya V. Karthik ([email protected]) Mar 2014, TAU, Santa Cruz 6/17

7 FSMs for Modeling Correlated Bits Correlated Bit sequence Analog (LTI) FSM Digital System Channel Arbitrary digital logic, arbitrary bit correlations Finite number of states For example, this FSM Arcs denoting state transitions can never produce the Each arc has an output bit sequence [0, 1, 1] Aadithya V. Karthik ([email protected]) Mar 2014, TAU, Santa Cruz 7/17

8 Algorithm for Correlated WC Eye Key idea: Best partial sum ending in state Si Aadithya V. Karthik ([email protected]) Mar 2014, TAU, Santa Cruz 8/17

9 Algorithm for Correlated WC Eye Key idea: Best partial sum ending in state Si Aadithya V. Karthik ([email protected]) Mar 2014, TAU, Santa Cruz 9/17

10 Algorithm for Correlated WC Eye Key idea: Best partial sum ending in state Si Aadithya V. Karthik ([email protected]) Mar 2014, TAU, Santa Cruz 10/17

11 Algorithm for Correlated WC Eye Key idea: Best partial sum ending in state Si Aadithya V. Karthik ([email protected]) Mar 2014, TAU, Santa Cruz 11/17

12 Algorithm for Correlated WC Eye Key idea: Best partial sum ending in state Si Aadithya V. Karthik ([email protected]) Mar 2014, TAU, Santa Cruz 12/17

13 Algorithm for Correlated WC Eye Key idea: Best partial sum ending in state Si Compare to PDA, which Dynamic programming pessimistically predicts 0.5 Aadithya V. Karthik ([email protected]) Mar 2014, TAU, Santa Cruz 13/17

14 Results: 8b/10b Encoder (1/2) 8b/10b Encoder + LTI Channel 8b parallel 8b/10b Encoder 10b serial LTI Channel Aadithya V. Karthik ([email protected]) Mar 2014, TAU, Santa Cruz 14/17

15 Results: 8b/10b Encoder (2/2) 8b/10b Encoder + LTI Channel Ours PDA Aadithya V. Karthik ([email protected]) Mar 2014, TAU, Santa Cruz 15/17

16 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 Aadithya V. Karthik ([email protected]) Mar 2014, TAU, Santa Cruz 16/17

17 Questions Aadithya V. Karthik ([email protected]) Mar 2014, TAU, Santa Cruz 17/17

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