scholarly journals Redundant Residue Number System Based Multiple Error Detection and Correction Using Chinese Remainder Theorem (CRT)

2017 ◽  
Vol 5 (5) ◽  
pp. 72
Author(s):  
Idris Abiodun Aremu ◽  
Kazeem Alagbe Gbolagade
Keyword(s):  
Error Detection ◽  
Chinese Remainder Theorem ◽  
Number System ◽  
Residue Number System ◽  
Error Detection And Correction ◽  
Residue Number ◽  
Redundant Residue Number System ◽  
Multiple Error

scholarly journals Multiple Error Correction in Redundant Residue Number Systems: A Modified Modular Projection Method with Maximum Likelihood Decoding

2022 ◽  
Vol 12 (1) ◽  
pp. 463
Author(s):  
Mikhail Babenko ◽  
Anton Nazarov ◽  
Maxim Deryabin ◽  
Nikolay Kucherov ◽  
Andrei Tchernykh ◽  
...  
Keyword(s):  
Error Detection ◽  
Chinese Remainder Theorem ◽  
Number System ◽  
Maximum Likelihood Decoding ◽  
Number Systems ◽  
Residue Number Systems ◽  
Error Detection And Correction ◽  
Residue Number ◽  
Weighted Number ◽  
Multiple Error

Error detection and correction codes based on redundant residue number systems are powerful tools to control and correct arithmetic processing and data transmission errors. Decoding the magnitude and location of a multiple error is a complex computational problem: it requires verifying a huge number of different possible combinations of erroneous residual digit positions in the error localization stage. This paper proposes a modified correcting method based on calculating the approximate weighted characteristics of modular projections. The new procedure for correcting errors and restoring numbers in a weighted number system involves the Chinese Remainder Theorem with fractions. This approach calculates the rank of each modular projection efficiently. The ranks are used to calculate the Hamming distances. The new method speeds up the procedure for correcting multiple errors and restoring numbers in weighted form by an average of 18% compared to state-of-the-art analogs.

Improved Lempel-Ziv-Welch’s Error Detection and Correction Scheme using Redundant Residue Number System (RRNS)

2017 ◽  
Vol 2 (6) ◽  
pp. 25-30 ◽  
Author(s):  
Alhassan Abdul- Barik ◽  
Mohammed Ibrahim Daabo ◽  
Stephen Akobre
Keyword(s):  
Error Detection ◽  
Dynamic Range ◽  
Number System ◽  
Residue Number System ◽  
Compression Scheme ◽  
Encrypted Data ◽  
Correction Scheme ◽  
Error Detection And Correction ◽  
Residue Number ◽  
Redundant Residue Number System

The greatest difficulty of compressing data is the assurance of the security, integrity, and accuracy of the data in storage in volatile media or transmission in network communication channels. Various methods have been proposed for dealing with the accuracy and consistency of compressed and encrypted data using error detection and correction mechanisms. The Redundant Residue Number System (RRNS) which is a trait of Residue Number System (RNS) is one of the available methods for detecting and correcting errors which involves the addition of extra moduli called redundant moduli. In this paper, Residue Number System (RNS) is efficiently applied to the Lempel-Ziv-Welch (LZW) compression algorithm resulting in new LZW-RNS compression scheme using the traditional moduli set, and two redundant moduli added resulting in the moduli set {2^n-1,〖 2〗^n,〖 2〗^n+1,〖 2〗^2n-3,〖 2〗^2n+1} for the purposes of error detection and correction. This is done by constraining the data or information within the legitimate range of the dynamic range provided by the non-redundant moduli. Simulation with MatLab shows the efficiency and fault tolerance of the proposed scheme than the traditional LZW compression method and other related known state of the art schemes.

scholarly journals Performance Enhancement of MIMO-OFDM using Redundant Residue Number System

2018 ◽  
Vol 8 (5) ◽  
pp. 3902
Author(s):  
M. I. Youssef ◽  
A. E. Emam ◽  
M. Abd Elghany
Keyword(s):  
Bit Error Rate ◽  
Error Rate ◽  
Error Detection ◽  
Orthogonal Frequency Division Multiplexing ◽  
Number System ◽  
Residue Number System ◽  
Error Detection And Correction ◽  
Residue Number ◽  
Mimo Ofdm ◽  
Redundant Residue Number System

Telecommunication industry requires high capacity networks with high data rates which are achieved through utilization of Multiple-Input-Multiple-Output (MIMO) communication along with Orthogonal Frequency Division Multiplexing (OFDM) system. Still, the communication channel suffers from noise, interference or distortion due to hardware design limitations, and channel environment, and to combat these challenges, and achieve enhanced performance; various error control techniques are implemented to enable the receiver to detect any possible received errors and correct it and thus; for a certain transmitted signal power the system would have lower Bit Error Rate (BER). The provided research focuses on Redundant Residue Number System (RRNS) coding as a Forward Error Correction (FEC) scheme that improves the performance of MIMO-OFDM based wireless communications in comparison with current methods as Low-Density Parity Check (LDPC) coders at the transmitter side or equalizers at receiver side. The Bit Error Rate (BER) performance over the system was measured using MATLAB tool for different simulated channel conditions, including the effect of signal amplitude reduction and multipath delay spreading. Simulation results had shown that RRNS coding scheme provides an enhancement in system performance over conventional error detection and correction coding schemes by utilizing the distinct features of Residue Number System (RNS).

scholarly journals Single and Multiple Error Detection and Correction using Redundant Residue Number System for Cryptographic and Stenographic Schemes

2020 ◽  
pp. 1-14
Author(s):  
Peter Awon-natemi Agbedemnab ◽  
Edward Yellakuor Baagyere ◽  
Mohammed Ibrahim Daabo
Keyword(s):  
Error Detection ◽  
Fault Tolerant ◽  
Number System ◽  
Residue Number System ◽  
Accurate Information ◽  
Transmission Errors ◽  
Error Detection And Correction ◽  
Residue Number ◽  
Efficient Scheme ◽  
Redundant Residue Number System

The possibility of errors being propagated during the encoding process of cryptographic and steganographic schemes is real due to the introduction of noise by ciphering the data from stage to stage. This real possibility therefore requires that an efficient scheme is proposed such that if after the decoding process the accurate information is not discovered, then it can be employed to detect and correct any errors in the system. The Residue Number System (RNS) by its nature is fault tolerant since an error in one digit position does not affect other digit positions; but the Redundant Residue Number System (RRNS) had been used over the years to effectively detect and correct errors. In this paper, we propose an efficient scheme that can detect and correct both single and multiple errors after and/or during computation and/or transmission provided the redundant moduli are sufficient enough. A theoretical analysis of the performance of the proposed scheme show it will be a better choice for detecting and correcting computational and transmission errors to existing similar state-of-the-art schemes.

scholarly journals An efficient implementation of the Chinese Remainder Theorem in minimally redundant Residue Number System

2020 ◽  
Vol 21 (2) ◽  
Author(s):  
Mikhail Selianinau
Keyword(s):  
Chinese Remainder Theorem ◽  
Number System ◽  
Residue Number System ◽  
Computer Applications ◽  
The Novel ◽  
Residue Modulo ◽  
Modern Computer ◽  
Residue Number ◽  
Novel Method ◽  
Redundant Residue Number System

The Chinese Remainder Theorem (CRT) widely used in many modern computer applications. This paper presents an efficient approach to the calculation of the rank of a number, a principal positional characteristic used in the Residue Number System (RNS). The proposed method does not use large modulo addition operations compared to a straightforward implementation of the CRT algorithm. The rank of a number is equal to a sum of an inexact rank and a two-valued correction factor that only takes on the values 0 or 1. We propose a minimally redundant RNS, which provides low computational complexity of the rank calculation. The effectiveness of the novel method is analyzed concerning conventional non-redundant RNS. Owing to the extension of the residue code, by adding the extra residue modulo 2, the complexity of rank calculation goes down from \(O(k^2)\) to \(O(k)\), where \(k\) equals the number of residues in non-redundant RNS.

scholarly journals An Enhanced Error Detection and Correction Scheme for Enterprise Resource Planning (ERP) Data Storage

2021 ◽  
pp. 72-90
Author(s):  
Arnold Mashud Abukari ◽  
Edem Kwedzo Bankas ◽  
Mohammed Muniru Iddrisu
Keyword(s):  
Data Storage ◽  
Data Access ◽  
Resource Planning ◽  
Number System ◽  
Residue Number System ◽  
Data Loss ◽  
Error Detection And Correction ◽  
Residue Number ◽  
Redundant Residue Number System ◽  
Access Data

In this research paper, a Redundant Residue Number System (n,k) code is introduced to enhance Cloud ERP Data storage. The research findings have been able to demonstrate the application  of Redundant Residue Number System (RRNS) in the concept of Cloud ERP Data storage. The scheme contributed in addressing data loss challenges during data transmission. The proposed scheme also addressed and improved the probability of failure to access data compared to other existing systems. The proposed scheme adopted the concept of Homomorphic encryption and secret sharing whiles applying Redundant Residue Number System to detect and correct errors.The moduli set used is {2m, 2m + 1, 2m+1 - 1, 2m+1 + 1, 2m+1 + k, 22m - k, 22m + 1} where k is the number of the information moduli set used. The information moduli set is {2m, 2m + 1, 2m+1 - 1} and the redundant moduli is {2m+1 + 1, 2m+1 + k, 22m - k, 22m + 1}. The proposed scheme per the simulation results using python reveals that it performs far better in terms of data loss and failure to access data related concerns. The proposed scheme performed better between 41.2% for data loss to about 99% for data access based on the combination of (2, 4) and (2, 5) data shares respectively in a (k, n) settings.

Optimized Parity-Based Error Detection and Correction Methods for Residue Number System

2018 ◽  
Vol 28 (01) ◽  
pp. 1950002 ◽  
Author(s):  
Adib Armand ◽  
Somayeh Timarchi ◽  
Hossein Mahdavi
Keyword(s):  
Fault Tolerance ◽  
Error Detection ◽  
High Speed ◽  
Fault Tolerant ◽  
Number System ◽  
Low Complexity ◽  
Residue Number System ◽  
Cell Library ◽  
Error Detection And Correction ◽  
Residue Number

Residue Number System (RNS) has been extensively used in high-speed applications. It inherits the advantages of parallelism and modularity, which lead to fault tolerance property. Since carry propagation is limited to each module in RNS, errors do not propagate inter-moduli. Indeed, due to the restriction in carry propagation and fault tolerance property, RNS can be promisingly fast and reliable that makes it a favorable encoding for the digital systems which are highly prone to noise like communication channels. By adding some extra moduli, the so-called redundant RNS (RRNS) is gained. Although several methods around RRNS have already been proposed in the literature, the structures without need for extra moduli have not been introduced yet. This paper addresses three Error Detection and Correction (EDC) schemes for RNS based on parity structures. Using these techniques, the low power fault-tolerant RNS methods with low complexity are presented. Synthesis results using 180[Formula: see text]nm CMOS standard cell library show that the proposed architectures for the three-moduli set [Formula: see text] are in average 17%, 52% and 44% more efficient than the conventional RRNS in terms of delay, power consumption, and area overhead, respectively, without losing the EDC capability.

scholarly journals Computationally Efficient Approach to Implementation of the Chinese Remainder Theorem Algorithm in Minimally Redundant Residue Number System

2021 ◽  
Author(s):  
Mikhail Selianinau
Keyword(s):  
Chinese Remainder Theorem ◽  
Number System ◽  
Residue Number System ◽  
Computer Applications ◽  
Efficient Approach ◽  
Residue Modulo ◽  
Modern Computer ◽  
New Variant ◽  
Residue Number ◽  
Residue Code

AbstractIn this paper, we deal with the critical problem of performing non-modular operations in the Residue Number System (RNS). The Chinese Remainder Theorem (CRT) is widely used in many modern computer applications. Throughout the article, an efficient approach for implementing the CRT algorithm is described. The structure of the rank of an RNS number, a principal positional characteristic of the residue code, is investigated. It is shown that the rank of a number can be represented by a sum of an inexact rank and a two-valued correction to it. We propose a new variant of minimally redundant RNS, which provides low computational complexity for the rank calculation, and its effectiveness analyzed concerning conventional non-redundant RNS. Owing to the extension of the residue code, by adding the excess residue modulo 2, the complexity of the rank calculation goes down from $O\left (k^{2}\right )$ O k 2 to $O\left (k\right )$ O k with respect to required modular addition operations and lookup tables, where k equals the number of non-redundant RNS moduli.

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