Impact of Process Variations on Computers Used for Image Processing

1. Impact of Process Variations on Computers Used for Image Processing SurajSindia, Fa Foster Dai, Vishwani D. Agrawal Auburn University, AL, USA Virendra Singh Indian Institute of Technology Bombay, Mumbai, India ISCAS 2012, Seoul, South Korea 22 May 2012

2. Outline • Why are computers becoming “noisy”? • Background & motivation • How can we model this noise? • Our work in this project • What is their impact on simple image processing operations? • Results

3. Transistor: Basic Building Block of Computers D D D ON OFF G VGS S S S VGS>VTH VGS<VTH Transistor: SWITCH (1) Transistors are used as switches. (2) Computers are built using complex logic networks of these switches.

4. Transistors Are Shrinking: Moore’s Law Strained Si High-K metal gate Fin FET Ref.: S. Borkar, “Design Perspectives in 22nm CMOS and Beyond,” DAC’09 Ref.: D. Patterson, et. al., “Big Data, HPC, and Cancer,” Intel Developer Forum’11

5. Manufacturing Variation in Transistors • As transistor dimensions shrink they no longer behave “exactly” as intended. • Random dopant fluctuation in transistor channel • Line edge roughness from lithography • Threshold Voltage, VTH, of two transistors on the same chip is no longer constant. Random dopant fluctuation Line Edge Roughness

6. Gate Delay and Threshold Voltage • Variation in transistor threshold voltage leads to variation in delay offered by logic gates built using such transistors VDD: Supply Voltage (constant) tD0: Delay offered by zero threshold voltage gate td: Delay offered by a logic gate

7. Histogram of VTH and td at L=32nm VTH(σ/μ)=16.82% Delay (σ/μ)=21.64% 150 120 100 80 60 40 20 0 150 120 100 80 60 40 20 0 No. of gates No. of gates 0.1 0.2 0.3 0.4 0.5 0.6 0.7 5 10 15 20 25 30 td (ns) VTH(V) Variation in delay offered by logic gates on a chip leads to errors in computation.

8. Evolution of VTH and td Variance 0.35 delay, td threshold voltage, VTH 0.30 0.25 0.20 Delay variation is increasing at a higher rate than variation in threshold voltage σ/μ 0.15 0.10 0.05 0 20 40 60 80 100 120 140 160 180 Effective channel length, L(nm)

9. Outline • Why are computers becoming “noisy”? • Background and motivation • How can we model this noise? • Our work in this project • What is their impact on simple image processing operations? • Results

10. Statistics of Computation Error Due to Underlying VTH Variation Log-Normal distribution of Delay (td) Statistics of errors in computation is deduced Normal distribution of VTH p(VTH) p(td) Delay in logic circuits 1 0 µDelay µVTH 0/1 thresholding due to flip flop metastability (Uniform distribution) Only if D > µDelay , else it is correct.

11. Synthesis of Unreliable Hardware 256×256 array Adder a0 a7 b0 b7 + + C7 C0 a N(1,σ) N(1,σ) b S’0 S’7 C’1 a Cout Cin Cin N(1,σ) Cin b a b S0 S7 + C1 a S S b Cout Cin Our Unit element 8 bits

12. Image Processing Tasks Used for System Simulation Low pass filtering or image smoothening 1/9 1/9 1/9 2D Convolution 1/9 1/9 1/9 1/9 1/9 1/9 Input image Convolution Mask Output image High pass filtering or Edge Enhancement -1 -1 -1 2D Convolution 0 24 0 1 1 1 Input image Convolution Mask Scaled output image

13. Analytical Model for Computation Noise 0 ,i ,i td,i: Delay offered by logic along ith bit line td,th : Maximum allowed delay across all bit lines. (Determined by operating clock frequency)

14. Outline • Why are computers becoming “noisy”? • Background and motivation • How can we model this noise? • Our work in this project • What is their impact on simple image processing operations? • Results

15. Low Pass Filtering: Comparison Across Different Technology Nodes Noisy image Processed image Processed on ideal computer without any process variation Processed on 45nm Processed on 32nm Processed on 22nm

16. High Pass Filtering: Comparison Across Different Technology Nodes Noisy image Processed image Processed on ideal computer without any process variation Processed on 45nm Processed on 32nm Processed on 22nm

17. SNR as a Function of Technology Node High pass filter Signal to Noise Ratio (dB) Low pass filter Threshold of visual tolerance Technology node (nm)

18. Recovering Images using Hardware Fault Tolerance • We notice that the images in the processed technologies have noise that is identified as salt-and-pepper type. • By using simple neural networks in hardware, we can recover these images online. [Sindia et. al. @ VTS’2012] Processed images on 22nm node SNR=17dB SNR=58dB With hardware fault tolerance Without hardware fault tolerance

19. Conclusion • We studied the impact of process variation in processors on common image processing tasks such as low pass and high pass filtering. • We synthesized an adder array of size 256 by 256 to study these image processing tasks. • We saw that there is a decrease in SNR of processed images by as much as 7.5dB with the advance of every technology node. • We motivated future work to recover images processed on computers where the underlying hardware has process variation. • We also proposed analytical model for process variation in underlying hardware manifesting as computation noise at a high level of abstraction.