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

TL;DR

This work addresses reliable data transfer from SFQ to CMOS by deploying a lightweight RM(1,3) ECC encoder implemented in SFQ logic, converting 4-bit messages to 8-bit codewords with the capability to correct one bit and detect up to three. It introduces a JoSIM-MATLAB co-simulation framework to quantify performance under process parameter variations and fabrication defects, operating at a representative cryogenic interface bandwidth. The RM(1,3) encoder occupies modest hardware resources (eight XORs, seven DFFs, and related splitters) and demonstrates improved error-free transmission probabilities over encoder-less designs, especially under moderate PPV, while enabling fault-tolerance analysis through the framework. Overall, the paper provides a practical, hardware-efficient ECC solution and a scalable evaluation flow for SFQ-to-CMOS interfaces with real-world variability and defect scenarios.

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.

Figures (6)

• Figure 1: Block diagram of a cryogenic digital output data link incorporating the SFQ-based RM(1,3) encoder and decoder. The schematic of RM(1,3) encoder is shown at the logic level using XOR gates, DFFs, and SFQ splitters (clock distribution network is not shown).
• Figure 2: Simulation results of the SFQ-based RM(1,3) code encoder operating at 5 GHz. SFQ-to-DC converters are used as an interface circuit.
• Figure 3: Block diagram of the proposed simulation framework for the analysis of RM(1,3) code encoder.
• Figure 4: CDF for receiving at most $N_\mathtt{err}$ erroneous messages. $N=100$ messages are transmitted with 1000 independent circuit realizations. Each realization has up to $\pm$20% PPV.
• Figure 5: CDF for receiving at most $N_\mathtt{err}$ erroneous messages with $\pm$20%, $\pm$15%, and $\pm$5% PPV values for RM(1,3) encoder. $N=100$ messages are transmitted with 1000 independent circuit realizations.