scholarly journals Design of Reed-Solomon Encoder for Error Detection in DRAM Cells

2021 ◽  
Author(s):  
Prateek Asthana ◽  
Gargi Khanna ◽  
Sahil Sankhyan ◽  
Tarun Chaudhary
Keyword(s):  
Error Detection ◽  
Structural Modeling ◽  
Galois Field ◽  
Code Word ◽  
Field Algebra ◽  
Module Design ◽  
Reed Solomon Codes ◽  
Complex Algorithm

This paper investigates the design of Reed Solomon (RS) encoder. Based on the message symbols, the RS encoder generates the code-word. By carrying out a polynomial division using Galois Field algebra, the parity symbols are calculated. Reed-Solomon codes are one of the most effective and effective non-binary error codes to detect and correct burst errors. This is the focus work for my dissertation to implement RS encoder and decoder that is a complex algorithm and it is used for the reliable memory operation in a system. The RS Encoder and decoder are design in structural modeling and develop the hardware. The sift and multiplier type divider is used for Encoder and Syndrome module design.

scholarly journals Optical Comparison Operation for 8-Bit QPSK-Modulated Signal by Using Serially-Cascaded Delay Line Interferometer

2018 ◽  
Vol 8 (9) ◽  
pp. 1440 ◽  
Author(s):  
Yohei Aikawa
Keyword(s):  
Error Detection ◽  
Communication Systems ◽  
Delay Line ◽  
Hamming Distance ◽  
Code Word ◽  
Modulation Format ◽  
Comparison Operation ◽  
Error Detection And Correction ◽  
All Optical ◽  
Shift Keying

An all-optical comparator is desirable to realize large-capacity, fully-transparent, and energy-efficient communication systems, as it is considered to be a fundamental component to perform most of the operations, including packet switching, label recognition, error detection and correction, and so on. However, most of the previous studies have been confined to the on–off keying (OOK) modulation format, not phase-shift keying (PSK) modulation. In this paper, the author provides a novel optical comparator designed for quadrature PSK (QPSK)-modulated signal, which comprises a code word with 8-bit length, using a serially-cascaded delay line interferometer. The proposed comparator yields constellations having the information of a Hamming distance based on the designed code, when several patterns of QPSK signal are injected into the comparator. The paper experimentally demonstrates the feasibility of the optical comparison operation for 8-bit QPSK-modulated return-to-zero (RZ) signal at 10 Gbaud.

scholarly journals Error correction by Reed–Solomon codes using its automorphisms

2021 ◽  
Vol 66 (1) ◽  
pp. 110-116
Author(s):  
V. A. Lipnitsky ◽  
S. I. Semyonov
Keyword(s):  
Error Correction ◽  
Galois Field ◽  
Correction Method ◽  
New Method ◽  
Group Of Automorphisms ◽  
Rs Codes ◽  
Reed Solomon Codes ◽  
Rs Code ◽  
Error Correction Method ◽  
Joint Group

The article explores the syndrome invariants of АГ-group of automorphisms of Reed–Solomon codes (RS-codes) that are a joint group of affine and cyclic permutations. The found real invariants are a set of norms of N Г-orbits that make up one or another АГ-orbit. The norms of Г-orbits are vectors with 2 1 Cδ− coordinates from the Galois field, that are determined by all kinds of pairs of components of the error syndromes. In this form, the invariants of the АГ-orbits were cumbersome and difficult to use. Therefore, their replacement by conditional partial invariants is proposed. These quasi-invariants are called norm-projections. Norm-projection uniquely identifies its АГ-orbit and therefore serves as an adequate way for formulating the error correction method by RS-codes based on АГ-orbits. The power of the АГ-orbits is estimated by the value of N2, equal to the square of the length of the RS-code. The search for error vectors in transmitted messages by a new method is reduced to parsing the АГ‑orbits, but actually their norm-projections, with the subsequent search for these errors within a particular АГ-orbit. Therefore, the proposed method works almost N2 times faster than traditional syndrome methods, operating on the basic of the “syndrome – error” principle, that boils down to parsing the entire set of error vectors until a specific vector is found.

Find balance, as in coding theory

2020 ◽  
pp. 211-216
Author(s):  
Susan D'Agostino
Keyword(s):  
Error Detection ◽  
Word Length ◽  
Coding Theory ◽  
Code Word ◽  
Transmission Time ◽  
Optimal Codes ◽  
Mathematics Students ◽  
The Right ◽  
Undesirable Outcome ◽  
Just Right

“Find balance, as in coding theory” explains how mathematicians construct codes to transmit messages as accurately and efficiently as possible. Since “noise” may corrupt messages during transmission, a good code repeats some of the information in a sent message so that errors due to noise in the received message may be detected and (ideally) corrected. However, too much repetition increases not only the code word length but the transmission time—an undesirable outcome. Mathematician Claude Shannon proved that “optimal” codes with just the right balance between repetition in transmission and error detection exist. Mathematics students and enthusiasts are encouraged to find a balance that is just right between repetition and forward momentum in mathematical and life pursuits. At the chapter’s end, readers may check their understanding by working on a problem concerning book International Standard Book Numbers (ISBNs). A solution is provided.

scholarly journals PERFORMANCE AND ANALYSIS OF REED-SOLOMAN CODES FOR EFFICIENT COMMUNICATION SYSTE

2013 ◽  
Vol 10 (1) ◽  
pp. 1249-1254
Author(s):  
Sagar Chouksey ◽  
Mayur Ghadle ◽  
Abdul Rasheed ◽  
Shaikh Khursheed Mohd Murtaza
Keyword(s):  
Wireless Communication ◽  
Error Detection ◽  
Communication System ◽  
Communication Systems ◽  
Error Rates ◽  
Solomon Code ◽  
Reed Solomon Codes ◽  
Reed Solomon Code ◽  
Wide Range ◽  
Error Detection And Correction

In wireless communication systems reducing bit/frame/symbol error rate is critical. If bit error rates are high then in wireless communication system our aim is to minimize error by employing various coding methods on the data transferred. Various channel coding for error detection and correction helps the communication system designers to reduce the effects of a noisy data transmission channel. In this paper our focus is to study and analysis of the performance of Reed-Solomon code that is used to encode the data stream in digital communication. The performances were evaluated by applying to different phase sift keying (PSK) modulation scheme in Noisy channel. Reed-Solomon codes are one of the best for correcting burst errors and find wide range of applications in digital communications and data storage. Reed-Solomon codes are good coding technique for error correcting, in which redundant information is added to data so that it can be recovered reliably despite errors in transmission or retrieval. The error correction system used is based on a Reed-Solomon code. These codes are also used on satellite and other communications systems. 

Application of constant-weight code "1-out-if-5" for the organization of combinational circuits check

2017 ◽  
pp. 307-319
Author(s):  
Valeriy Sapozhnikov ◽  
Vladimir Sapozhnikov ◽  
Dmitriy Efanov ◽  
Dmitriy Pyvovarov
Keyword(s):  
Error Detection ◽  
Practical Importance ◽  
Discrete Systems ◽  
Code Word ◽  
Technical Diagnostics ◽  
Concurrent Error Detection ◽  
Combinational Circuits ◽  
Constant Weight ◽  
Testing Patterns ◽  
Full Check

Objective: To study specificities of “1-out of-5”equilibrium code application in the process of concurrent error detection of combinational logic circuits organization. Methods: Information and coding theories, as well as technical diagnostics of discrete systems were applied. Results: It was suggested to apply a “1-out of-5”equilibrium code in organizing of combinational circuits control by means of Boolean complement method, the tester of which has a simple structure and needs five testing patterns for its full check. The calculation method of Boolean complement functions was given; the former makes it possible to provide testability of a Boolean complement block and a tester within a checking circuit. The advantages of a “1-out of-5”equilibrium code application were presented, compared to the usage of other equilibrium codes with a shorter length of a code word for organization of combinational circuits’ check. Practical importance: The application of a “1-out of-5”equilibrium code for organization of combinational circuits’ check is promising for self-checking discrete automatic and calculating machines.

scholarly journals SYNTHESIS METHODS OF SELF-CHECKING COMBINATIONAL DEVICES OF AUTOMATIC CONTROLS BASED ON LOGICAL COMPLEMENT TO THE EQUILIBRIUM 1-OUT-OF 4 CODE

2021 ◽  
Vol 7 (4) ◽  
pp. 645-668
Author(s):  
D. V. Efanov ◽  
◽  
G. V. Osadchy ◽  
I. V. Leskovets ◽  
◽  
...  
Keyword(s):  
Error Detection ◽  
Integrated Control ◽  
Experimental Studies ◽  
Basic Structure ◽  
Code Word ◽  
Control Circuit ◽  
Synthesis Methods ◽  
Digital Devices ◽  
Control Schemes ◽  
Control Circuits

The article is devoted to the development of the logical complement method for the synthesis of self-checking digital devices and systems. The article highlights the features of using the equilibrium 1-out-of 4 code for the synthesis of integrated control circuits of combinational logic devices by the method of logical complement. The basic structures of the organization of built-in control schemes by the method of logical complement to the equilibrium 1-out-of 4 code are described and several ways of organizing control schemes are considered. The fi rst one implies the control of devices with the allocation of outputs fours and the use of conversion of three outputs out of four in the basic structure. There is another way of organizing the control circuit by the method of logical complement to the equilibrium code and it involves the search for outputs triplets and their addition to the four-digit code word of the 1-out-of 4 code by directly connecting the output of the supervisor logic block to the tester input without any signal conversion. The third method is associated with the use of a basic structure with the circuit for the preliminary signal compression from the unit under test and the reduced number of outputs control. The article presents the results of experimental studies for each of the methods of organizing the built-in control circuit and estimates the structures technical implementation complexity as well as the probability of detecting errors at the outputs of the unit under test when single-stuck faults are introduced. In many cases the logical complement method allows to synthesize simpler self-checking devices compared to the duplication method with high rates of error detection at the unit under test outputs.

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