Error correction of digital signal processing devices using non-positional modular codes

Kaplun, Dmitry; Klionskiy, Dmitry M.; Bogaevskiy, D. V.; Gulvanskiy, V. V.; Veligosha, A. V.; Kalmykov, Igor A.

doi:10.3103/s0146411617030051

Cited by 9 publications

(3 citation statements)

References 3 publications

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“…The sequence of arithmetic operations required to calculate the output sample of the filter, in accordance with the difference equation [17], is a chain of basic operations over the low-bit quantities (reminders) α i , described by Equation (4)…”

Section: Methodsmentioning

confidence: 99%

Optimization of the FIR Filter Structure in Finite Residue Field Algebra

et al. 2018

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This paper introduces a method for optimizing non-recursive filtering algorithms. A mathematical model of a non-recursive digital filter is proposed and a performance estimation is given. A method for optimizing the structural implementation of the modular digital filter is described. The essence of the optimization is that by using the property of the residue ring and the properties of the symmetric impulse response of the filter, it is possible to obtain a filter having almost a half the length of the impulse response compared to the traditional modular filter. A difference equation is given by calculating the output sample of modules p1 … pn in the modified modular digital filter. The performance of the modular filters was compared with the performance of positional non-recursive filters implemented on a digital signal processor. An example of the estimation of the hardware costs is shown to be required for implementing a modular digital filter with a modified structure. This paper substantiates the expediency of applying the natural redundancy of finite field algebra codes on the example of the possibility to reduce hardware costs by a factor of two. It is demonstrated that the accuracy of data processing in the modular digital filter is higher than the accuracy achieved with the implementation of filters on digital processors. The accuracy advantage of the proposed approach is shown experimentally by the construction of the frequency response of the non-recursive low-pass filters.

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Section: Methodsmentioning

confidence: 99%

Optimization of the FIR Filter Structure in Finite Residue Field Algebra

et al. 2018

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“…Since the basic operation of digital filtration is the sum of binary products, then [10,11] described digital filters operating in RNS. Application of RNS codes for detection and correction of errors occurring during computations was described in [7,12]. It is proposed in [13] to apply RNS codes for error correction upon transfer of well telemetric data.…”

Section: Modular Codes Of Residue Number Systemmentioning

confidence: 99%

Redundant Modular Codes for Development of Fault-Tolerant Systems of Satellite Identification

Kalmykov¹

2020

IJETER

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Hydrocarbon production in the Extreme North on unattended facilities is based on low earth orbit satellite (LEOS) systems for communications. Their information security can be improved by means of Identification-Friend-or-Foe (IFF) system for satellite. Authentication protocol based on modular codes(MC) makes it possible prior to communicating session to determine satellite status at minimum time consumptions. Such result is achieved due to parallel computations based on MC. However, MC can also detect and correct errors. Therefore, development of authentication protocol, where redundant MC are used for correction of errors occurring upon calculation of response to request from identification system, is an urgent problem. This work is aimed at improvement of fault tolerance of satellite identification system by means of the developed authentication protocol, where redundant MC are used for correction of errors occurring upon calculation of response to request from interrogator.

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“…Therefore, one of the ways to significantly increase the speed and decrease the computing power in these algorithms is to utilize the residue number system. RNS usually is used for applications such as digital signal processing [11,12], digital filters [13,14], image processing [15,16], and error correction systems [17,18].…”

Section: Introductionmentioning

confidence: 99%

Efficient Implementation Of The Sum Of Residues Modular Reduction Using Arithmetic-Friendly RNS Moduli Set

Alvani

2024

EATP

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Introduction: Due to the importance of public-key cryptography in information and communication security, it is widely employed in various applications for secure communication. Materials and Methods: multiplication and exponentiation of large numbers are used in cryptography algorithms such as RSA, ElGamal, and elliptic curve cryptography. Results and Discussion: The residue number system in these algorithms is very efficient since calculations are performed on small residues, resulting in a fast arithmetic operation, as well as lower power consumption. The modular reduction of large numbers is one of the main operations in most public-key cryptography systems, which includes large computations in finite fields. This paper presents an efficient implementation of modular reduction. To this end, arithmetic-friendly moduli were selected and employed in the implementation of the improved sum of residues reduction algorithm. The SOR algorithm using the proposed moduli set was described in VHDL language and synthesized on the Xilinx virtex7 FPGA family using ISE14.7 software. Conclusion:The results showed that, compared to the recent similar works, the implementation of the improved sum of residues algorithm using the proposed moduli set has achieved higher speed and uses less hardware resources.

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Error correction of digital signal processing devices using non-positional modular codes

Cited by 9 publications

References 3 publications

Optimization of the FIR Filter Structure in Finite Residue Field Algebra

Optimization of the FIR Filter Structure in Finite Residue Field Algebra

Redundant Modular Codes for Development of Fault-Tolerant Systems of Satellite Identification

Efficient Implementation Of The Sum Of Residues Modular Reduction Using Arithmetic-Friendly RNS Moduli Set

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