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.

翻译：在单磁通量子逻辑等超导数字电子器件向半导体电路传输数据的过程中，磁通俘获、工艺参数波动以及制造缺陷等因素会导致比特错误。本文设计并分析了一种轻量化的硬件高效纠错编码器。具体而言，采用SFQ数字逻辑实现了里德-穆勒码RM(1,3)编码器。所提出的RM(1,3)编码器可将4位信息转换为8位码字，分别能够检测和纠正最多3位和1位错误。该编码器电路基于MIT-LL SFQ5ee工艺和SuperTools/ColdFlux RSFQ单元库进行设计。为研究RM(1,3)编码器的性能，提出了集成JoSIM仿真器与MATLAB脚本的自动化数据采集与分析仿真框架。在±20%工艺参数波动条件下，相较于无编码器设计，所提出的编码器将无误码概率提升了6.7%。当工艺参数波动控制在±15%及以下时，该编码器能以至少99.1%的概率纠正全部错误。此外，借助所提出的框架研究了开路故障等制造缺陷对编码器电路的影响。