Deterministic Shuffling Networks to Implement Stochastic Circuits in Parallel

Zhiheng Wang, Devan Larso, Morgen Barker, Soheil Mohajer, Kia Bazargan

Research output: Contribution to journalArticlepeer-review


Stochastic computing (SC) in recent years has been defined as a digital computation approach that operates on streams of random bits that represent probability values. SC can perform complex tasks with much smaller hardware footprints compared with conventional binary methods, but previous methods on SC circuits operated on serial bit streams, which leads to high-latency implementations. This article presents a significant improvement over previous work; it provides a deterministic parallel bit shuffling network that can use a simple deterministic thermometer encoding of data, resulting in zero random fluctuation and high accuracy, yet keeping the output bit-stream length constant. We use core 'stochastic' logic circuits that do not employ constant coefficients, making them significantly smaller than traditional stochastic logic that use a significant amount of resources to generate such coefficients. Our experiments show that compared with previous SC methods, our method has up to 3× smaller mean absolute error, and better area × delay and power efficiency. Compared with conventional binary methods, our method is better in terms of area × delay at 8-bit resolution. It shows better power efficiency (40×, 18×, and 8× Gops/W at 8-, 10-, and 12-bit resolutions) compared with conventional binary.

Original languageEnglish (US)
Article number9119189
Pages (from-to)1821-1832
Number of pages12
JournalIEEE Transactions on Very Large Scale Integration (VLSI) Systems
Issue number8
StatePublished - Aug 2020

Bibliographical note

Funding Information:
Manuscript received July 23, 2019; revised November 29, 2019 and February 21, 2020; accepted March 10, 2020. Date of publication June 16, 2020; date of current version July 30, 2020. This work was supported in part by the National Science Foundation under Grant 1408123 (CCF-SHF). (Corresponding author: Zhiheng Wang.) Zhiheng Wang is with the University of Minnesota Twin Cities, Minneapolis, MN 55455 USA (e-mail:

Publisher Copyright:
© 1993-2012 IEEE.


  • Low power application
  • power efficient computation
  • stochastic computation (SC)


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