1. SoC Design Lab, Electronic Engineering, National Changhua University of Education, Taiwan, R.O.C 1 2009/11/30 Presenter: Pin-Chong Chen Advisor: Tsung-Che Huang Low-Cost CLT-Based Random Number Generator for Communication Test

2. SoC Design Lab, Electronic Engineering, National Changhua University of Education, Taiwan, R.O.C 2 References Y.-H. Chou, T.-H. Wu and T.-C. Huang, “Low-Cost CLT-based Random Number Generator for Communication Test,”VLSI Test Technology Workshop (VTTW), Test Applications, pp.79-82, Taiwan, Jul. 2009.

3. SoC Design Lab, Electronic Engineering, National Changhua University of Education, Taiwan, R.O.C 3 Outline Introduction Previous Work Random Number Generator (RNG)  Normal Distribution RNG  Uniform Distribution RNG Programmable Delay Line (PDL)  Coarse-tuned PDL  Fine-tuned PDL Experiment Results Conclusions

4. SoC Design Lab, Electronic Engineering, National Changhua University of Education, Taiwan, R.O.C 4 Introduction In high-speed computer and communication systems, timing jitter is one of the most critical parameters. Jitter testing is becoming indispensable. Conventional Jitter Generator is executed by expensive external testers or instruments. This paper develop a CLT-based Random Number Generator for Communication test.

5. SoC Design Lab, Electronic Engineering, National Changhua University of Education, Taiwan, R.O.C 5 Ideal and Jitter Waveform Waveform transition is too early Waveform transition is too late Ideal Waveform Jitter is defined as the short-term variations of a digital signal’s significant instants from their ideal positions in time. Fig. 1 Jitter Waveforms

6. SoC Design Lab, Electronic Engineering, National Changhua University of Education, Taiwan, R.O.C 6 RNG (Screening Sampling) Box-Muller Ziggurat Algorithm Fig. 2 Typical Ziggurat Algorithm (1)

7. SoC Design Lab, Electronic Engineering, National Changhua University of Education, Taiwan, R.O.C 7 RNG (Direct Sampling) Table LookUp Fig. 3 Typical Table LookUp Methods

8. SoC Design Lab, Electronic Engineering, National Changhua University of Education, Taiwan, R.O.C 8 Conventional CLT-based RNG Fig. 4 A Conventional CLT-based RNG The conventional CLT approves the sum of m independent random variables with uniform distribution, it will be approaching to a normal distribution.

9. SoC Design Lab, Electronic Engineering, National Changhua University of Education, Taiwan, R.O.C 9 Proposed CLT-based RNG Fig. 5 Proposed CLT-based RNG Where k is a non-negative integer

10. SoC Design Lab, Electronic Engineering, National Changhua University of Education, Taiwan, R.O.C 10 LFSR-based Uniform Distribution RNG/JG Fig. 6 Uniform Distribution RNG Fig. 7 Uniform Distribution Jitter Generator

11. SoC Design Lab, Electronic Engineering, National Changhua University of Education, Taiwan, R.O.C 11 CPDL Fig. 8 Coarse-tuned Programmable Delay Line The jitter distribution control block can include several XOR gates for a uniform distribution RNG or be normal distribution RNG.

12. SoC Design Lab, Electronic Engineering, National Changhua University of Education, Taiwan, R.O.C 12 FPDL Fig. 9 Fine-tuned Programmable Delay Line

13. SoC Design Lab, Electronic Engineering, National Changhua University of Education, Taiwan, R.O.C 13 Proposed CLT Layout Fig. 10 Layout of a CLT-based RNG TSMC 0.13um CMOS 1P8M The proposed CLT RNG sourced from 12 type-I 16- bit LFSR. MethodCore Area Conventional CLT22896.45 Proposed CLT10776.28 47% area reduce Table 1 Area Comparisons

14. SoC Design Lab, Electronic Engineering, National Changhua University of Education, Taiwan, R.O.C 14 Randomness: Scatter Diagram Fig. 11 Scatter diagrams with 10,000 entries of 16-bit outputs

15. SoC Design Lab, Electronic Engineering, National Changhua University of Education, Taiwan, R.O.C 15 Goodness of Fit Fig. 12 Fitting Sampled Number to a Normal Distribution In Communication test, the fitness is more critical than the randomness. (2)

16. SoC Design Lab, Electronic Engineering, National Changhua University of Education, Taiwan, R.O.C 16 Experiment Results Table 2 Comparison of Proposed Conventional CLT-based RNGs

17. SoC Design Lab, Electronic Engineering, National Changhua University of Education, Taiwan, R.O.C 17 Conclusions In this paper we proposed a theorem to reduce the parallel counter in conventional type-I LFSR-sourced CLT-based RNG to a parallel 1’s counter. More than 93% of counter area can be saved mainly due to the reduced register length for a 16-bit fraction system. About 47% of area and 30% of adder levels, namely the propagation time can be reduced. We proposed a jitter generator embedded in network on-a-chip or system-in-a-package for communication test.

18. SoC Design Lab, Electronic Engineering, National Changhua University of Education, Taiwan, R.O.C 18 Thanks for your attention.