Evaluation of Fast Sample Entropy Algorithms on FPGAs: From Performance to Energy Efficiency

Chao Chen; Bruno da Silva; Ruiqi Chen; Shun Li; Jianqing Li; Chengyu Liu

doi:10.3390/e24091177

Evaluation of Fast Sample Entropy Algorithms on FPGAs: From Performance to Energy Efficiency

Entropy (Basel). 2022 Aug 23;24(9):1177. doi: 10.3390/e24091177.

Authors

Chao Chen^{1

2}, Bruno da Silva², Ruiqi Chen³, Shun Li⁴, Jianqing Li¹, Chengyu Liu¹

Affiliations

¹ School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China.
² Department of Electronics and Informatics (ETRO), Vrije Universiteit Brussel (VUB), 1050 Brussels, Belgium.
³ VeriMake Research, Nanjing Renmian Integrated Circuit Technology Co., Ltd., Nanjing 210096, China.
⁴ College of Physics and Information Engineering, Fuzhou University, Fuzhou 350108, China.

Abstract

Entropy is one of the most fundamental notions for understanding complexity. Among all the methods to calculate the entropy, sample entropy (SampEn) is a practical and common method to estimate time-series complexity. Unfortunately, SampEn is a time-consuming method growing in quadratic times with the number of elements, which makes this method unviable when processing large data series. In this work, we evaluate hardware SampEn architectures to offload computation weight, using improved SampEn algorithms and exploiting reconfigurable technologies, such as field-programmable gate arrays (FPGAs), a reconfigurable technology well-known for its high performance and power efficiency. In addition to the fundamental disclosed straightforward SampEn (SF) calculation method, this study evaluates optimized strategies, such as bucket-assist (BA) SampEn and lightweight SampEn based on BubbleSort (BS-LW) and MergeSort (MS-LW) on an embedded CPU, a high-performance CPU and on an FPGA using simulated data and real-world electrocardiograms (ECG) as input data. Irregular storage space and memory access of enhanced algorithms is also studied and estimated in this work. These fast SampEn algorithms are evaluated and profiled using metrics such as execution time, resource use, power and energy consumption based on input data length. Finally, although the implementation of fast SampEn is not significantly faster than versions running on a high-performance CPU, FPGA implementations consume one or two orders of magnitude less energy than a high-performance CPU.

Keywords: FPGAs; complexity; electrocardiogram (ECG); performance; power efficiency; reconfigurable computing; sample entropy; time series.

Grants and funding

This research was funded by the National Key Research and Development Program of China (2019YFE0113800), the National Natural Science Foundation of China (62171123, 62071241, 62001111 and 81871444), the Distinguished Young Scholars of Jiangsu Province (BK20190014), China Scholarship Council (202106090175).