TRUE‐BSG: A True Random Bit-Stream Generator for Fast and Efficient Stochastic Computing

Mehran Moghadam¹, Shelby Williams², Abu Kaisar Mohammad Masum²,�M. Hassan Najafi¹, Sercan Aygun², and Magdy Bayoumi²

¹Electrical, Computer, and Systems Engineering Department, Case Western Reserve University, Cleveland, OH, USA

²School of Computing and Informatics, University of Louisiana at Lafayette, Lafayette, LA, USA

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• Introduction
• Stochastic Computing
• Motivation for True Randomness
• Overview of TRUE-BSG
• Design Details
• Performance Evaluations
• Hardware Cost & Energy Efficiency
• Application – Image Compositing
• Conclusion

TRUE-BSG: A True Random Bit-Stream Generator for Fast and Efficient Stochastic Computing

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Outline

Stochastic Computing (SC)

• Re-emerging computing paradigm – approximate computing
• Long bit-stream representation vs binary representation
• No bit significant - Equal weight for all digits
• Mapping Scalar value to the probability of occurring ‘1’s in the bit-stream
• Arithmetic operations via simple logic gates
• Multiplication via single AND gate considering uncorrelated inputs

TRUE-BSG: A True Random Bit-Stream Generator for Fast and Efficient Stochastic Computing

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11110000, 10101010, 11001010,…

SC Bit-Streams

Binary to SC conversion

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Introduction

TRUE-BSG: A True Random Bit-Stream Generator for Fast and Efficient Stochastic Computing

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Limitations of Existing Random Number Generators (RNGs):

• Pseudo-RNGs (e.g., LFSRs): Deterministic, risk bias and correlation.

• Quasi-RNGs (e.g., Sobol sequences): Improved randomness yet incur high hardware cost.

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True Random Number Generators (TRNGs):

• Exploit unpredictable physical phenomena (thermal/quantum noise).

• Deliver high entropy and minimal correlation, ideal for SC.

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Need: A fast, energy-efficient TRNG tailored for SC applications.

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Motivations for True Randomness

Core Idea:

• Integrates a high-quality TRNG based on ring oscillators.

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Key Attributes:

• Speed: Generates random bits at 1 Gbps (GHz speed vs. MHz for state-of-the-art works).
• Quality: Provides true randomness with high entropy.
• Efficiency: Offers energy-efficient bit-stream generation suited for resource-constrained systems.

TRUE-BSG: A True Random Bit-Stream Generator for Fast and Efficient Stochastic Computing

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Overview of TRUE-BSG

TRNG Architecture:

• Utilizes ring oscillators with multiplexers and nine selection bits.

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Modes of Operation:

• MetaStability (MS): Initializes by setting outputs to a known state.
• Ring Oscillator Modes (RO3 & RO5): �Switch modes to extract randomness via metastability and jitter.

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Operation Flow:

• Mode transitions (MS → RO3/RO5 → MS) extract high-entropy bits for SC bit-stream generation.

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TRUE-BSG: A True Random Bit-Stream Generator for Fast and Efficient Stochastic Computing

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Design Details

TRUE-BSG: A True Random Bit-Stream Generator for Fast and Efficient Stochastic Computing

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Novel approach for Generating desired SC bit-streams

from a single TRNG stream

Comparison of SC bit-stream generation accuracy

Performance Evaluation

Mean Absolute Error (MAE) decreases with increased bit-stream length.

Converting 100,000 inputs in [0,1] into SC bit-streams.

Performance Evaluation of MAE

TRUE-BSG: A True Random Bit-Stream Generator for Fast and Efficient Stochastic Computing

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SC Arithmetic Operations:

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• Comparable accuracy to Software-based built-in RNG with improved true randomness.

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Hardware Cost & Energy Efficiency of Number Generators

Synthesis Results (45nm Technology):

• Area: 223 µm²
• Energy: 34 fJ per random bit

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Comparison:

• 8-bit LFSR: 167 µm²; 299 fJ per bit
• 8-bit Sobol: 941 µm²; 600 fJ per bit

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Advantage:

• Significant energy savings (8.8× to 17.6× lower energy per bit) with competitive area footprint.

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TRUE-BSG: A True Random Bit-Stream Generator for Fast and Efficient Stochastic Computing

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Application – Image Compositing

Case Study:

• Image compositing (blending foreground and background) using a MUX.

TRUE-BSG: A True Random Bit-Stream Generator for Fast and Efficient Stochastic Computing

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Conclusion & Impact

Contributions:

• TRNG-based bit-stream generator delivering fast (1 Gbps), energy-efficient, high-quality randomness.
• Enhances SC accuracy and robustness while lowering hardware energy costs.

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Implications:

• Ideal for next-generation low-power, fault-tolerant, highly parallel SC systems (edge and resource-constrained applications).

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Future Directions:

• Further integration with SC architectures and exploration of additional application domains.

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TRUE-BSG: A True Random Bit-Stream Generator for Fast and Efficient Stochastic Computing

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TRUE-BSG: A True Random Bit-Stream Generator for Fast and Efficient Stochastic Computing

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Thanks for your attention!

Questions:

Mehran Moghadam

moghadam@case.edu

This paper: