VLSI Implementation of a Cost-Efficient Loeffler DCT Algorithm with Recursive CORDIC for DCT-Based Encoder
Abstract
:1. Introduction
2. The Image Compression Algorithm
2.1. JPEG
2.2. DCT
2.3. 2-D DCT Using Row-Column 1-D DCT Architecture
2.4. CORDIC Algorithm
2.5. Loeffler DCT Algorithm with Recursive CORDIC
3. VLSI Architecture
4. Experimental Results of the Proposed Loeffler DCT Algorithm with Recursive CORDIC
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Scale Factor | Quantization Value | Quantization Erorr | Add | Shift |
---|---|---|---|---|
0 | 0 | 1 | ||
4 | 5 | |||
3 | 4 |
Iteration (i) | Angle = 3π/8 | Angle = 3π/16 | Angle = π/16 |
---|---|---|---|
0 | σ = 1 | σ = 1 | σ = 1 |
1 | σ = 1 | σ = −1 | σ = −1 |
2 | σ = −1 | σ = 1 | σ = −1 |
3 | σ = 1 | σ = 1 | σ = 1 |
4 | σ = 1 | σ = −1 | σ = −1 |
5 | σ = −1 | σ = −1 | σ = 1 |
6 | σ = 1 | σ = −1 | σ = 1 |
7 | σ = 1 | σ = 1 | σ = 1 |
8 | σ = −1 | σ = −1 | σ = 1 |
9 | σ = −1 | σ = 1 | σ = −1 |
10 | σ = 1 | σ = 1 | σ = 1 |
Loeffler [28] | Sun [29] | Lee [30] | This Work | |
---|---|---|---|---|
Airplane | 35.85 | 34.83 | 35.48 | 35.84 |
Splash | 37.72 | 37.02 | 37.42 | 37.70 |
Lena | 34.51 | 33.96 | 34.37 | 34.50 |
Mandrill | 27.61 | 27.13 | 27.40 | 27.60 |
Girl | 34.68 | 34.29 | 34.48 | 34.67 |
House | 33.74 | 32.76 | 33.31 | 33.72 |
Peppers | 33.25 | 32.82 | 33.07 | 33.24 |
Sailboat | 31.04 | 30.49 | 30.85 | 31.04 |
Average | 33.55 | 32.91 | 33.30 | 33.54 |
Loeffler [28] | Sun [29] | Lee [30] | This Work | |
---|---|---|---|---|
Kodak01 | 28.57 | 27.99 | 28.33 | 28.56 |
Kodak02 | 32.93 | 32.58 | 32.81 | 32.92 |
Kodak03 | 34.33 | 33.86 | 34.17 | 34.32 |
Kodak04 | 33.10 | 32.55 | 32.96 | 33.09 |
Kodak05 | 28.87 | 27.91 | 28.57 | 28.86 |
Kodak06 | 30.02 | 29.49 | 29.81 | 30.00 |
Kodak07 | 33.94 | 32.93 | 33.71 | 33.93 |
Kodak08 | 28.35 | 27.37 | 27.86 | 28.34 |
Kodak09 | 33.84 | 33.01 | 33.59 | 33.83 |
Kodak10 | 33.62 | 32.86 | 33.36 | 33.61 |
Kodak11 | 30.81 | 30.27 | 30.61 | 30.80 |
Kodak12 | 33.96 | 33.32 | 33.71 | 33.94 |
Kodak13 | 26.25 | 25.67 | 26.02 | 26.24 |
Kodak14 | 30.12 | 29.51 | 29.94 | 30.19 |
Kodak15 | 32.88 | 32.33 | 32.62 | 32.87 |
Kodak16 | 32.32 | 31.99 | 32.19 | 32.31 |
Kodak17 | 32.73 | 32.13 | 32.52 | 32.72 |
Kodak18 | 29.52 | 28.93 | 29.32 | 29.51 |
Kodak19 | 31.35 | 30.59 | 31.02 | 31.34 |
Kodak20 | 32.72 | 32.03 | 32.42 | 32.71 |
Kodak21 | 30.40 | 29.78 | 30.16 | 30.40 |
Kodak22 | 31.39 | 30.92 | 31.23 | 31.38 |
Kodak23 | 35.84 | 34.95 | 35.57 | 35.82 |
Kodak24 | 29.27 | 28.61 | 29.00 | 29.26 |
Average | 31.55 | 30.90 | 31.31 | 31.54 |
DCT Type | Multiply | Add | Shift |
---|---|---|---|
Loeffler DCT [28] | 22 | 58 | 8 |
Sun [29] | 0 | 120 | 92 |
Lee [30] | 0 | 192 | 172 |
This work without hardware sharing machine | 0 | 108 | 96 |
This work with hardware sharing machine | 0 | 28 | 11 |
Original | Loeffler [28] | Sun [29] | Lee [30] | |
---|---|---|---|---|
Lena | ||||
PSNR | 34.51 dB | 33.96 dB | 34.37 dB | |
Kodak03 | ||||
PSNR | 34.33 dB | 33.96 dB | 34.37 dB |
Performance Metric | Sun et al. [29] | Lee et al. [30] | Kim et al. [36] | Wu et al. [37] | This Study |
---|---|---|---|---|---|
PSNR (dB) | 30.90 | 31.31 | 31.49 | 31.55 | 31.54 |
Compression Ratio | 9.86 | 9.86 | 9.86 | 9.86 | 9.86 |
Process (µm) | TSMC 0.13 | TSMC 0.13 | TSMC 0.13 | TSMC 0.13 | UMC 0.18 |
Operating Frequency (MHz) | 100 | 100 | 100 | 100 | 100 |
Gate Count (k) | 27.30 | 22.40 | 24.60 | 31.50 | 8.04 |
Power (mW) | 6.54 | 5.11 | 5.42 | 5.62 | 4.17 |
Core Area (µm2) | 255 k | 209.2 k | 229.8 k | 294.2 k | 75.1 k |
Memory | 96 | 96 | 96 | 96 | 96 |
Normalized Gate Count | 3.40 | 2.79 | 3.06 | 3.92 | 1.00 |
FOM | 11.16 | 13.78 | 12.62 | 9.88 | 38.68 |
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Chung, R.-L.; Chen, C.-W.; Chen, C.-A.; Abu, P.A.R.; Chen, S.-L. VLSI Implementation of a Cost-Efficient Loeffler DCT Algorithm with Recursive CORDIC for DCT-Based Encoder. Electronics 2021, 10, 862. https://doi.org/10.3390/electronics10070862
Chung R-L, Chen C-W, Chen C-A, Abu PAR, Chen S-L. VLSI Implementation of a Cost-Efficient Loeffler DCT Algorithm with Recursive CORDIC for DCT-Based Encoder. Electronics. 2021; 10(7):862. https://doi.org/10.3390/electronics10070862
Chicago/Turabian StyleChung, Rih-Lung, Chen-Wei Chen, Chiung-An Chen, Patricia Angela R. Abu, and Shih-Lun Chen. 2021. "VLSI Implementation of a Cost-Efficient Loeffler DCT Algorithm with Recursive CORDIC for DCT-Based Encoder" Electronics 10, no. 7: 862. https://doi.org/10.3390/electronics10070862