Abstract
Multipliers are ubiquitous among the core components of multiple signal processing systems. Stochastic computing provides an alternative method to lower the design complexity and power consumption of multipliers, relying on independently and identically distributed bitstreams. In this chapter, several stochastic multipliers are reviewed, evaluated, and applied to image processing algorithms. Serial stochastic multipliers with serial bit-wise operations consume too long computing time and thus more energy. Parallel stochastic multipliers using hard-wired connections tackle this issue to shorten processing time, at a cost of occupied footprint. In addition, deterministic approaches, including relatively prime stream length, rotation, and clock division, are applied to stochastic multipliers to realize completely exact computing results, with double computing time.
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References
J.V. Neumann, Probabilistic logics and the synthesis of reliable organisms from unreliable components, in Automata Studies, ed. by C.E. Shannon, J. McCarthy, (Princeton University Press, Princeton, 1956), pp. 43–98
B. Gaines, “Stochastic Computing,” presented at the Proceedings of the Spring Joint Computer Conference on – AFIPS’67, Atlantic City, New Jersey, 18–20 Apr 1967
W. Poppelbaum, C. Afuso, J. Esch, “Stochastic computing elements and systems,” presented at the Proceedings of the Fall Joint Computer Conference on – AFIPS’67, Anaheim, California, 14–16 Nov., 1967
S. Ribeiro, Random-pulse machines. IEEE Trans. Electron. Comput. EC-16(3), 261–276 (Jun 1967)
B. Brown, H. Card, Stochastic neural computation I: Computational elements. IEEE Trans. Comput. 50(9), 891–905 (2001)
W. Gross, V. Gaudet, Stochastic Computing: Techniques and Applications (Springer, 2019)
P. Meher, T. Stouraitis, Arithmetic circuits for DSP applications (Wiley, Hoboken, 2017)
F. Zhu, S. Zhen, X. Yi, H. Pei, B. Hou, Y. He, Design of approximate radix-256 booth encoding for error-tolerant computing. IEEE Trans. Circuits Syst. II-Exp. Brief. 69(4), 2286–2290 (Apr 2022)
A. Alaghi, J. Hayes, “Exploiting correlation in stochastic circuit design,” presented at the 2013 IEEE 31st International Conference on Computer Design (ICCD), Asheville, 6–9 Oct 2013
R. Budhwani, R. Ragavan, O. Sentieys, “Taking advantage of correlation in stochastic computing,” presented at the 2017 IEEE International Symposium on Circuits and Systems (ISCAS), Baltimore, 28–31 May 2017
W. Qian, X. Li, M. Riedel, K. Bazargan, D. Lilja, An architecture for fault-tolerant computation with stochastic logic. IEEE Trans. Comput. 60(1), 93–105 (Jan 2011)
S. Salehi, Low-cost stochastic number generators for stochastic computing. IEEE Trans. Very Large Scale Integ. (Vlsi) Syst. 28(4), 992–1001 (Apr 2020)
H. Sim, J. Lee, “Cost-effective stochastic MAC circuits for deep neural networks,” Neural Networks vol. 117, pp. 152–162, Sep. 2019
Y. Zhang et al., “A parallel Bitstream generator for stochastic computing,” presented at the 2019 Silicon Nanoelectronics Workshop, Kyoto, 9–10 June 2019
Y. Zhang, L. Xie, J. Han, X. Cheng, G. Xie, Highly accurate and energy efficient binary-stochastic multipliers for fault-tolerant applications. IEEE Trans. Circuits Syst. II: Exp. Brief. 70(2), 771–775 (2023)
Y. Zhang, R. Wang, X. Zhang, Y. Wang, R. Huang, “Parallel hybrid stochastic-binary-based neural network accelerators,” IEEE Trans. Circuits Syst. II: Exp. Brief, vol. 67, no. 12, pp. 3387–3391, Dec. 2020
The USC-SIPI Image Database. Available: https://sipi.usc.edu/database/
Z. Wang, A. Bovik, H. Sheikh, E. Simoncelli, Image quality assessment: From error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (Apr 2004)
C. Solomon, T. Breckon, Fundamentals of digital image processing: a practical approach with examples in matlab (Wiley, The Atrium, Southern Gate, Chichester, 2011)
M. Ansari, H. Jiang, B. Cockburn, J. Han, Low-power approximate multipliers using encoded partial products and approximate compressors. IEEE J. Emerg. Select. Topic. Circuit. Syst. 8(3), 404–416 (2018)
D. Jenson, M. Riedel, “A deterministic approach to stochastic computation,” presented at the 2016 IEEE/ACM International Conference on Computer-Aided Design, Austin, 7–10 Nov 2016
M. Najafi, S. Jamali-Zavareh, D. Lilja, M. Riedel, K. Bazargan, R. Harjani, An overview of time-based computing with stochastic constructs. IEEE Micro 37(6), 62–71 (Nov–Dec 2017)
Z. Lin, G. Xie, W. Xu, J. Han, Y. Zhang, Accelerating stochastic computing using deterministic Halton sequences. IEEE Trans. Circuit. Syst. II-Exp. Brief. 68(10), 3351–3355 (Oct 2021)
H. Najafi, D. Lilja, High quality down-sampling for deterministic approaches to stochastic computing. IEEE Trans. Emerg. Top. Comput. 9(1), 7–14 (Mar 2018)
S. Liu, J. Han, “Energy efficient stochastic computing with Sobol sequences,” presented at the Design, Automation & Test in Europe Conference & Exhibition (DATE), 2017, Lausanne, 27–31 Mar 2017
M. Najafi, D. Lilja, M. Riedel, “Deterministic methods for stochastic computing using low-discrepancy sequences,” presented at the 2018 IEEE/ACM International Conference on Computer-Aided Design (ICCAD), San Diego, 5–8 Nov 2018
A. Alaghi, J. Hayes, “Fast and accurate computation using stochastic circuits,” presented at the 2014 Design, Automation & Test in Europe Conference & Exhibition (DATE), Dresden, 24–28 Mar 2014
Nangate open cell library. Available: https://projects.si2.org. (2014, Jun 18)
A. Alaghi, L. Cheng, J. Hayes, “Stochastic circuits for real-time image-processing applications,” presented at the 2013 50th ACM/EDAC/IEEE Design Automation Conference (DAC), Austin, 29 May – 7 Jun 2013
J. Bersen, “Dynamic thresholding of grey-level images,” presented at the Eighth International Conference on Pattern Recognition, Paris, 27–31 Oct 1986
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Zhang, Y., Han, J., Xie, G. (2024). Stochastic Multipliers: from Serial to Parallel. In: Liu, W., Han, J., Lombardi, F. (eds) Design and Applications of Emerging Computer Systems. Springer, Cham. https://doi.org/10.1007/978-3-031-42478-6_9
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