Small-Area Sorting Network Based on Unary Coding Using Single Flux Quantum Circuits

The sorting network is crucial in fields like communication switching, data mining, image processing, neural networks, and others, where the bitonic sorting network (BSN) is an efficient comparison sorting method. It uses the compare-and-swap (CAS) units to compare two input data and decide whether to swap them. The single flux quantum (SFQ) circuits are well known for their high-speed operation and low power consumption, but they are less effective at performing numerical comparisons in CAS units. To address this issue, the unary coding (UC) method, an entropy encoding method that represents the natural number n with n ones followed by zeros, is introduced to implement a smaller SFQ-based BSN. The UC requires only AND and OR gates for CAS unit implementation. Consequently, the 8-input 32-bit UC BSN is two orders of magnitude smaller than the conventional SFQ binary coding BSN with the same precision and achieves approximately 3.3 times better energy efficiency. Additionally, compared to the CMOS-based UC BSN circuit, the energy efficiency improves by 5.8 times, even considering the cooling cost (×400). We also implemented a 4-input BSN circuit, using the 1.0 μm 10-layer Nb SFQ circuit fabrication process, and verified its operation at low speed.