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 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.

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 Algorithm for Clustering the Moduli of RNS for the Application of Optimization of Time Complexity in Standard Cipher System

2020 ◽  
Vol 9 (7) ◽  
pp. 92-97
Keyword(s):  
High Speed ◽  
High Performance ◽  
Fault Tolerant ◽  
Number System ◽  
Residue Number System ◽  
New Method ◽  
Residue Number ◽  
Residue Numbers ◽  
Performance Computing ◽  
Selection Of

Residue number system (RNS) has emerged as a knocking field of research due to its high speed, fault tolerant, carry free and parallel characteristics. Due to these features it has got important role in high performance computing especially with reduced delay. There are various algorithms have been found as a result of the research with respect to RNS. Additionally, since RNS reduces word length due to the modular operations, its computations are faster compared to binary computations. But the major challenges are the selection of moduli sets for the forward (decimal to residue numbers) and reverse (residue numbers to decimal) conversion. RNS performance is purely depending on how efficiently an algorithm computes / chooses the moduli sets [1]-[6]. This paper proposes new method for selecting the moduli sets and its usage in cryptographic applications based on Schonhage modular factorization. The paper proposes six moduli sets {6qk1, 6qk+1, 6qk+3, 6qk+5, 6qk+7, 6qk+11} for the RNS conversions but the Schonhage moduli sets are expressed as the exponents that creates a large gap between the moduli’s computed. Hence, a new method is proposed to for computing moduli sets that helps in representing all the decomposed values approximately in the same range.

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 HDL Implementation of Five Moduli Residue Number System

2019 ◽  
Vol 8 (9) ◽  
pp. 689-693
Keyword(s):  
High Speed ◽  
Fault Tolerant ◽  
Number System ◽  
Residue Number System ◽  
Verilog Hdl ◽  
Forward Converter ◽  
Half Adder ◽  
Ripple Carry Adder ◽  
Residue Number ◽  
Day By Day

The demand for residue number system (RNS) is increasing day by day because of its high speed and fault tolerant characteristics. RNS encodes a large number into group of small numbers, which consequently increases the overall data processing rate. This paper presents an analysis of the forward converter designed using ripple carry adder (RCA), carry save adder (CSA), and half adder-like (HAL), for the figure of merits area, delay, and power for five moduli set: 2n -1, 2n , 2n +1, 2n+1 -1, and 2n-1 -1 with the standard cells at 90 nm technology. The designing of different blocks has been done in Verilog-HDL. The area, delay, and power of the implemented circuits are obtained using the Synopsys Design Compiler at 90 nm technology node, while VCS is used for verification. It is observed that the area of the architecture using CSA is less, whereas power utilization and timing behavior are better in HAL.

scholarly journals Constant-coefficient FIR filters based on residue number system arithmetic

2012 ◽  
Vol 9 (3) ◽  
pp. 325-342 ◽  
Author(s):  
Negovan Stamenkovic ◽  
Vladica Stojanovic
Keyword(s):  
Power Dissipation ◽  
High Speed ◽  
Finite Impulse Response ◽  
Number System ◽  
Residue Number System ◽  
Fir Filter ◽  
Fir Filters ◽  
Residue Number ◽  
Low Power Dissipation ◽  
Residue Arithmetic

In this paper, the design of a Finite Impulse Response (FIR) filter based on the residue number system (RNS) is presented. We chose to implement it in the (RNS), because the RNS offers high speed and low power dissipation. This architecture is based on the single RNS multiplier-accumulator (MAC) unit. The three moduli set {2n+1,2n,2n-1}, which avoids 2n+1 modulus, is used to design FIR filter. A numerical example illustrates the principles of residue encoding, residue arithmetic, and residue decoding for FIR filters.

Sign in / Sign up

Export Citation Format

Share Document