Reed-Muller Error-Correction Code Encoder for SFQ-to-CMOS Interface Circuits

2026-02-11

AI Summary

This work addresses bit errors in the transfer of superconducting single-flux-quantum (SFQ) logic signals to CMOS circuits, which arise from flux trapping, process variations, and manufacturing defects. The paper presents the first lightweight RM(1,3) Reed–Muller encoder implemented in SFQ circuitry, encoding 4-bit messages into 8-bit codewords capable of detecting up to three errors and correcting one. Designed using the MIT-LL SFQ5ee process and SuperTools/ColdFlux cell libraries, the encoder’s robustness is evaluated through an automated simulation framework integrating JoSIM and MATLAB. Experimental results demonstrate a 6.7% improvement in error-free probability under ±20% process variation, with error correction success exceeding 99.1% for variations within ±15%. The study also effectively quantifies the impact of manufacturing defects such as open circuits.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Satisfiability
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

Data transmission from superconducting digital electronics such as single flux quantum (SFQ) logic to semiconductor (CMOS) circuits is subject to bit errors due to, e.g., flux trapping, process parameter variations (PPV), and fabrication defects. In this paper, a lightweight hardware-efficient error-correction code encoder is designed and analyzed. Particularly, a Reed-Muller code RM(1,3) encoder is implemented with SFQ digital logic. The proposed RM(1,3) encoder converts a 4-bit message into an 8-bit codeword and can detect and correct up to 3- and 1-bit errors, respectively. This encoder circuit is designed using MIT-LL SFQ5ee process and SuperTools/ColdFlux RSFQ cell library. A simulation framework integrating JoSIM simulator and MATLAB script for automated data collection and analysis, is proposed to study the performance of RM(1,3) encoder. The proposed encoder improves the probability of having no bit errors by 6.7% as compared to an encoder-less design under $\pm20\%$ PPV. With $\pm15\%$ and lower PPV, the proposed encoder could correct all errors with at least 99.1% probability. The impact of fabrication defects such as open circuit faults on the encoder circuit is also studied using the proposed framework.

Problem

• bit errors
• SFQ-to-CMOS interface
• process parameter variations
• fabrication defects
• flux trapping

Innovation

• Reed-Muller code
• SFQ-to-CMOS interface
• error-correction encoder
• RSFQ logic
• process parameter variation