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).

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