• 대한임베디드공학회논문지
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• 제16권5호
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• pp.233-240
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• 2021

We propose a novel, highly accurate approximate multiplier using different types of inexact 4-2 compressors. The importance of low hardware costs leads us to develop approximate multiplication for error-resilient applications. Several rules are developed when selecting a topology for designing the proposed multiplier. Our highly accurate multiplier design considers the different error characteristics of adopted compressors, which achieves a good error distribution, including a low relative error of 0.02% in the 8-bit multiplication. Our analysis shows that the proposed multiplier significantly reduces power consumption and area by 45% and 26%, compared with the exact multiplier. Notably, a trade-off relationship between error characteristics and hardware costs can be achieved when considering those of existing highly accurate approximate multipliers. In the image blending, edge detection and image sharpening applications, the proposed 8-bit approximate multiplier shows better performance in terms of image quality metrics compared with other highly accurate approximate multipliers.

• 한국전자통신학회논문지
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• 제17권4호
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• pp.671-678
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• 2022

근사 컴퓨팅은 정확한 결과 대신에 허용 가능한 정도의 부정확한 결과를 도출하는 연산 기법이다. 근사 곱셈은 고성능, 저전력 컴퓨팅을 위한 근사 컴퓨팅 방식 중 하나이다. 본 논문에서는 근사 4-2 compressor와 향상된 전가산기를 사용하여 고집적·저전력·고속 근사 곱셈기를 제안하였다. 근사 4-2 compressor를 사용한 근사 곱셈기는 정확, 근사, 상수 수정 영역의 3개 영역으로 구성되어 있으며, 효율적인 부분 곱 감소 방식을 적용하여 각 영역의 크기를 조절하면서 성능을 비교하였다. 제안한 근사 곱셈기는 Verilog HDL로 설계하였고, 25nm CMOS 공정에서 Synopsys Design Compiler(DC)를 이용하여 면적, 전력, 지연시간을 분석하였으며, 기존의 근사 곱셈기에 비해 면적을 10.47%, 전력을 26.11%, 지연시간을 13% 줄였다.

• 한국전자통신학회논문지
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• 제17권1호
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• pp.173-180
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• 2022

근사 컴퓨팅은 효율적인 하드웨어 컴퓨팅 시스템을 설계하기 위한 유망한 방법이다. 근사 곱셈은 고성능, 저전력 컴퓨팅을 위한 근사 계산 방식에 사용되는 핵심적인 연산이다. 근사 4-2 compressor는 근사 곱셈을 위한 효율적인 하드웨어 회로를 구현할 수 있다. 본 논문에서는 저면적, 저전력 특성을 갖는 근사 곱셈기를 제안하였다. 근사 곱셈기 구조는 정확한 영역, 근사 영역, 상수 수정 영역의 세 영역으로 나누어진다. 새로운 4:2 근사 compressor를 사용하여 근사 영역의 부분 곱 축소를 단순화하고, 간단한 오류 수정 방식을 사용하여 근사로 인한 오류를 보상한다. 상수 수정 영역은 오차를 줄이기 위해 확률 분석을 통한 상수를 사용하였다. 8×8 곱셈기에 대한 실험 결과, 제안한 근사 곱셈기는 기존의 4-2 compressor 기반의 근사 곱셈기보다 적은 면적을 요구하면서 적은 전력을 소비함을 보였다.

• ETRI Journal
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• 제43권4호
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• pp.684-693
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• 2021

This paper presents a low-cost two-stage approximate multiplier for bfloat16 (brain floating-point) data processing. For cost-efficient approximate multiplication, the first stage implements Mitchell's algorithm that performs the approximate multiplication using only two adders. The second stage adopts the exact multiplication to compensate for the error from the first stage by multiplying error terms and adding its truncated result to the final output. In our design, the low-cost multiplications in both stages can reduce hardware costs significantly and provide low relative errors by compensating for the error from the first stage. We apply our approximate multiplier to the convolutional neural network (CNN) inferences, which shows small accuracy drops with well-known pre-trained models for the ImageNet database. Therefore, our design allows low-cost CNN inference systems with high test accuracy.

• 대한수학회지
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• 제54권4호
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• pp.1063-1079
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• 2017

Two standard Bessel sequences in a Hilbert $C^*$-module are approximately duals if the distance (with respect to the norm) between the identity operator on the Hilbert $C^*$-module and the operator constructed by the composition of the synthesis and analysis operators of these Bessel sequences is strictly less than one. In this paper, we introduce (a, m)-approximate duality using the distance between the identity operator and the operator defined by multiplying the Bessel multiplier with symbol m by an element a in the center of the $C^*$-algebra. We show that approximate duals are special cases of (a, m)-approximate duals and we generalize some of the important results obtained for approximate duals to (a, m)-approximate duals. Especially we study perturbations of (a, m)-approximate duals and (a, m)-approximate duals of modular Riesz bases.

• ETRI Journal
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• 제39권2호
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• pp.145-150
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• 2017

As wearable devices are powered by batteries, they need to consume as little energy as possible. To address this challenge, in this article, we propose a synergistic technique for energy-efficient approximate speech signal processing (ASSP) for wearable devices. More specifically, to enable the efficient trade-off between energy consumption and sound quality, we synergistically integrate an approximate multiplier and a successive approximate register analog-to-digital converter using our enhanced conversion algorithm. The proposed ASSP technique provides ~40% lower energy consumption with ~5% higher sound quality than a traditional one that optimizes only the bit width of SSP.

• 전기전자학회논문지
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• 제26권4호
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• pp.736-741
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• 2022

격자 기반 암호화는 최악의 경우를 기반으로 한 강력한 보안, 비교적 효율적인 구현 및 단순성을 누리기 때문에 포스트 양자 암호화 방식 중 가장 실용적인 방식이다. 오류가 있는 링 학습(R-LWE)은 격자 기반 암호화(LBC)의 공개키암호화(Public Key Encryption: PKE) 방식이며, R-LWE의 가장 중요한 연산은 링의 모듈러 다항식 곱셈이다. 본 논문은 R-LWE 암호 시스템의 중간 보안 수준의 매개 변수 집합을 대상으로 하여 근사 컴퓨팅(Approximate Computing: AC) 기술을 기반으로 한 모듈러 곱셈기를 최적화하는 방법을 제안한다. 먼저 복잡한 로직을 간단하게 구현하는 방법으로 LUT을 사용하여 근사 곱셈 연산 중 일부의 연산 과정을 생략하고, 2의 보수 방법을 활용하여 입력 데이터의 값을 이진수로 변환 시 값이 1인 비트의 개수를 최소화하여 필요한 덧셈기의 개수를 절감하는 총 두 가지 방법을 제안한다. 제안된 LUT 기반의 모듈식 곱셈기는 기존 R-LWE 모듈식 곱셈기 대비 속도와 면적 모두 9%까지 줄어들었고, 2의 보수 방법을 적용한 모듈식 곱셈기는 면적을 40%까지 줄이고 속도는 2% 향상되는 것으로 나타났다. 마지막으로 이 두 방법을 모두 적용한 최적화된 모듈식 곱셈기의 면적은 기존대비 43%까지 감소하고 속도는 10%까지 감소하는 것으로 나타났다.

• 대한기계학회논문집A
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• 제22권4호
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• pp.811-825
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• 1998

An approximate line search is presented for dynamic response optimization with Augmented Lagrange Multiplier(ALM) method. This study empolys the approximate a augmented Lagrangian, which can improve the efficiency of the ALM method, while maintaining the global convergence of the ALM method. Although the approximate augmented Lagragian is composed of only the linearized cost and constraint functions, the quality of this approximation should be good since an approximate penalty term is found to have almost second-order accuracy near the optimum. Typical unconstrained optimization algorithms such as quasi-Newton and conjugate gradient methods are directly used to find exact search directions and a golden section method followed by a cubic polynomial approximation is empolyed for approximate line search since the approximate augmented Lagrangian is a nonlinear function of design variable vector. The numberical performance of the proposed approach is investigated by solving three typical dynamic response optimization problems and comparing the results with those in the literature. This comparison shows that the suggested approach is robust and efficient.

• 대한임베디드공학회논문지
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• 제15권5호
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• pp.235-242
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• 2020

This paper analyzes the effect of reduced output width of the truncated logarithmic multiplication and application to inferences using convolutional neural networks (CNNs). For small hardware overhead, output width is reduced in the truncated Mitchell multiplier, so that fractional bits in multiplication output are minimized in error-resilient applications. This analysis shows that when reducing output width in the truncated Mitchell multiplier, even though worst-case relative error increases, average relative error can be kept small. When adopting 8 fractional bits in multiplication output in the evaluations, there is no significant performance degradation in target CNNs compared to existing exact and original Mitchell multipliers.

• Journal of Information Processing Systems
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• 제19권3호
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• pp.377-384
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• 2023

The existence of abnormal breakpoint data leads to poor channel balance in wireless sensor networks (WSN). To enhance the communication quality of WSNs, a method for positioning abnormal breakpoint data in WSNs on the basis of signal reconstruction is studied. The WSN signal is collected using compressed sensing theory; the common part of the associated data set is mined by exchanging common information among the cluster head nodes, and the independent parts are updated within each cluster head node. To solve the non-convergence problem in the distributed computing, the approximate term is introduced into the optimization objective function to make the sub-optimization problem strictly convex. And the decompressed sensing signal reconstruction problem is addressed by the alternating direction multiplier method to realize the distributed signal reconstruction of WSNs. Based on the reconstructed WSN signal, the abnormal breakpoint data is located according to the characteristic information of the cross-power spectrum. The proposed method can accurately acquire and reconstruct the signal, reduce the bit error rate during signal transmission, and enhance the communication quality of the experimental object.