Research challenges in next-generation residue number system architectures

The residue number system (RNS) is a non-positional number system that allows one to perform addition and multiplication operations fast and in parallel. However, because the RNS is a non-positional number system, magnitude comparison of numbers in RNS form is impossible, so a division operation and an operation of reverse conversion into a positional form containing magnitude comparison operations are impossible too. Therefore, RNS has disadvantages in that some operations in RNS, such as reverse conversion into positional form, magnitude comparison, and division of numbers are problematic. One of the approaches to solve this problem is using the diagonal function (DF). In this paper, we propose a method of RNS construction with a convenient form of DF, which leads to the calculations modulo 2 n , 2 n − 1 or 2 n + 1 and allows us to design efficient hardware implementations. We constructed a hardware simulation of magnitude comparison and reverse conversion into a positional form using RNS with different moduli sets constructed by our proposed method, and used different approaches to perform magnitude comparison and reverse conversion: DF, Chinese remainder theorem (CRT) and CRT with fractional values (CRTf). Hardware modeling was performed on Xilinx Artix 7 xc7a200tfbg484-2 in Vivado 2016.3 and the strategy of synthesis was highly area optimized. The hardware simulation of magnitude comparison shows that, for three moduli, the proposed method allows us to reduce hardware resources by 5.98-49.72% in comparison with known methods. For the four moduli, the proposed method reduces delay by 4.92-21.95% and hardware costs by twice as much by comparison to known methods. A comparison of simulation results from the proposed moduli sets and balanced moduli sets shows that the use of these proposed moduli sets allows up to twice the reduction in circuit delay, although, in several cases, it requires more hardware resources than balanced moduli sets. such as field-programmable gate array (FPGA) and application-specific integrated circuit (ASIC). All these attractive features increase interest to RNS in the areas where large amounts of computation are needed. The applications of RNS are digital signal processing [2][3][4], cryptography [5][6][7], digital image processing [8], cloud computing [9], Internet of Things [10] and others. In [11], the authors propose a technique to estimate real-valued numbers by means of the Chinese remainder theorem (CRT), employing for this goal a Kroenecker based M-Estimation, to improve robustness. A new method based on the Chinese remainder theorem (CRT) is proposed for absolute position computation in [12]. This has advantages in terms of hardware and flexibility because it does not use memory. The authors of [13] offer to use RNS to improve the performance of the convolutional neural network developed for pattern recognition tasks. Reference [14] describes the method of construction for finite impulse response filers using RNS.However, the limitations of RNS include some operations such a...

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“…We only consider the most important practical cases, for example, when RNS contains three, four or five moduli [41]. Case 1.…”

Section: Rns With Odd Modulimentioning

confidence: 99%

Construction of Residue Number System Using Hardware Efficient Diagonal Function

et al. 2019

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“…The main RNS problems include the complexity of comparison of two numbers, division, reverse conversion and some other operations [10]. However, despite these disadvantages, RNS can be efficiently implemented in those applications where the basic calculations are multiplications combined with additions and subtractions.…”

Section: Introductionmentioning

confidence: 99%

FIR Filters in Two-Stage Residue Number System

Chervyakov

Lyakhov

Shulzhenko

2014

2014 International Conference on Engineering and Telecommunication

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This paper proposes a new approach to the implementation of Finite Impulse Response (FIR) filters in the Residue Number System (RNS). The essence of the method is to use the two-stage RNS, wherein uses two RNS: first RNS for transforming the input signal, and the second RNS for transforming of computational channels of the first RNS. This approach significantly reduces bit width of data, however, it requires to perform additional operations of forward and reverse conversion. Nevertheless modeling of FIR filters using the proposed architecture showed reducing the processing time in comparison with the known analogues.

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“…One of the most important issues of the RNS theory is to identify the best moduli set for a particular application [7]. Moduli set selection has an important role in RNS operations and may also impact on the application where is used [8].…”

Section: Introductionmentioning

confidence: 99%

Effect of RNS moduli set selection on digital filter performance for satellite communications

Chervyakov

Lyakhov

Kalita

et al. 2015

2015 International Siberian Conference on Control and Communications (SIBCON)

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The paper presents the results of investigation of RNS moduli set selection effect on the digital filters performance in satellite communication systems. Parks-McClellan filters with the order from 8 to 63 and 7 the most balanced RNS moduli sets were investigated. It is shown which of the considered moduli sets provide the best performance for such systems. Simultaneously difference in performance between the various moduli sets can be up to 32%.

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Research challenges in next-generation residue number system architectures

Cited by 29 publications

References 25 publications

Construction of Residue Number System Using Hardware Efficient Diagonal Function

Construction of Residue Number System Using Hardware Efficient Diagonal Function

FIR Filters in Two-Stage Residue Number System

Effect of RNS moduli set selection on digital filter performance for satellite communications

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