Lightweight Error-Correction Code Encoders in Superconducting Electronic Systems

TL;DR

This work tackles bit errors in cryogenic SFQ-to-room-temperature links caused by flux trapping, fabrication defects, and process-parameter variations. It proposes and hardware-implements lightweight ECC encoders based on $Hamming(7,4)$, $Hamming(8,4)$, and RM$(1,3)$ to protect a 4-bit message transmitted over an 8-bit codeword. Using a JoSIM+MATLAB framework, the study evaluates performance under PPV and finds $Hamming(8,4)$ provides the best practical protection with a zero-error probability of up to $92.7\%$, while RM$(1,3)$ offers competitive performance at the cost of more logic elements. The results offer guidance for designing reliable, low-area cryogenic data links in SFQ-based systems, balancing error-correction strength against circuit complexity and PPV sensitivity.

Abstract

Data transmission from superconducting electronic circuits, such as single flux quantum (SFQ) logic, to room-temperature electronics is susceptible to bit errors, which may result from flux trapping, fabrication defects, and process parameter variations (PPV). Due to the cooling power budget at 4.2 K and constraints on the chip area, the size of the error-correction code encoders is limited. In this work, three lightweight error-correction code encoders are proposed that are based on Hamming(7,4), Hamming(8,4), and Reed-Muller(1,3) codes and implemented with SFQ logic. The performance of these encoders is analyzed in the presence of PPV. The trade-offs between the theoretical complexity and physical size of error-correction code encoders are identified.

Figures (5)

• Figure 1: Block diagram of a cryogenic digital output data link incorporating an error-correction code encoder and decoder. CMOS amplifier circuits (not shown) may be included on the CMOS chip to boost the amplitude of the received signals.
• Figure 2: Schematic of a Hamming(8,4) code encoder implemented with SFQ logic. All XOR and DFF cells are clocked, though clock lines are not shown.
• Figure 3: Simulation results of a Hamming(8,4) code encoder operating at 5 GHz. Thermal noise at 4.2 K is added.
• Figure 4: Schematic of an RM(1,3) code encoder implemented with SFQ logic. All XOR and DFF cells are clocked (not shown).
• Figure 5: CDF representing the probability of receiving at most $N$ erroneous messages out of 100 transmissions. Each message was transmitted 1,000 times under independently sampled process variations, with each iteration incorporating up to ±20% variation in process parameters (set by JoSIM simulator).