Decoding algorithms with maximum error correction

2002 ◽  
Author(s):  
W.E. Stark ◽  
A.A. Hassan
Keyword(s):  
Error Correction ◽  
Maximum Error ◽  
Decoding Algorithms

scholarly journals Hamming Codes: Error Reducing Techniques

2021 ◽  
Vol 9 (11) ◽  
pp. 1972-1974
Author(s):  
Rohitkumar R Upadhyay
Keyword(s):  
Lower Bound ◽  
Error Correction ◽  
Coding Theory ◽  
Hamming Distance ◽  
Error Reduction ◽  
Error Correcting Codes ◽  
Significant Other ◽  
Hamming Codes ◽  
Decoding Algorithms ◽  
Reducing Properties

Abstract: Hamming codes for all intents and purposes are the first nontrivial family of error-correcting codes that can actually correct one error in a block of binary symbols, which literally is fairly significant. In this paper we definitely extend the notion of error correction to error-reduction and particularly present particularly several decoding methods with the particularly goal of improving the error-reducing capabilities of Hamming codes, which is quite significant. First, the error-reducing properties of Hamming codes with pretty standard decoding definitely are demonstrated and explored. We show a sort of lower bound on the definitely average number of errors present in a decoded message when two errors for the most part are introduced by the channel for for all intents and purposes general Hamming codes, which actually is quite significant. Other decoding algorithms are investigated experimentally, and it generally is definitely found that these algorithms for the most part improve the error reduction capabilities of Hamming codes beyond the aforementioned lower bound of for all intents and purposes standard decoding. Keywords: coding theory, hamming codes, hamming distance

“Soft Error” Correction Method Based on Low Complexity Coding and Encoding Algorithm

2014 ◽  
Vol 556-562 ◽  
pp. 6344-6349
Author(s):  
Yan Kang Wei ◽  
Da Ming Wang ◽  
Wei Jia Cui
Keyword(s):  
Fault Tolerance ◽  
Error Correction ◽  
Fault Tolerant ◽  
Low Complexity ◽  
Correction Method ◽  
Block Codes ◽  
Decoding Algorithms ◽  
Linear Block Codes ◽  
Data Errors ◽  
Linear Block

SEU is one of the major challenges affecting the reliability of computers on-board. In this paper, we design a kind of encoding and decoding algorithms with a low complexity based on the data correction method to resolve the data stream errors SEU may bring. Firstly, we use the theory of linear block codes to analyze various methods of data fault tolerance, and then from the encoding and decoding principle of linear block codes we design a kind of encoding and decoding algorithms with a low complexity of linear block code, The fault-tolerant coding method can effectively correct single-bit data errors caused by SEU, with low fault-tolerant overhead. Fault injection experiments show that: this method can effectively correct data errors caused by single event upset. Compared with other common error detection or correction methods, error correction performance of this method is superior, while its fault tolerance cost is less.

scholarly journals A Quaternary Code Correcting a Burst of at Most Two Deletion or Insertion Errors in DNA Storage

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1592
Author(s):  
Thi-Huong Khuat ◽  
Sunghwan Kim
Keyword(s):  
Error Correction ◽  
Data Storage ◽  
Upper Bounds ◽  
Code Design ◽  
Lower And Upper Bounds ◽  
Decoding Algorithms ◽  
Quaternary Code ◽  
Quaternary Codes ◽  
Dna Storage ◽  
Dna Strands

Due to the properties of DNA data storage, the errors that occur in DNA strands make error correction an important and challenging task. In this paper, a new code design of quaternary code suitable for DNA storage is proposed to correct at most two consecutive deletion or insertion errors. The decoding algorithms of the proposed codes are also presented when one and two deletion or insertion errors occur, and it is proved that the proposed code can correct at most two consecutive errors. Moreover, the lower and upper bounds on the cardinality of the proposed quaternary codes are also evaluated, then the redundancy of the proposed code is provided as roughly 2log48n.

scholarly journals Strictly local one-dimensional topological quantum error correction with symmetry-constrained cellular automata

2018 ◽  
Vol 4 (1) ◽  
Author(s):  
Nicolai Lang ◽  
Hans Peter Büchler
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Error Correction ◽  
Quantum Error Correction ◽  
One Dimensional ◽  
Decoding Algorithms ◽  
Topological Quantum ◽  
The One ◽  
Quantum Error

Active quantum error correction on topological codes is one of the most promising routes to long-term qubit storage. In view of future applications, the scalability of the used decoding algorithms in physical implementations is crucial. In this work, we focus on the one-dimensional Majorana chain and construct a strictly local decoder based on a self-dual cellular automaton. We study numerically and analytically its performance and exploit these results to contrive a scalable decoder with exponentially growing decoherence times in the presence of noise. Our results pave the way for scalable and modular designs of actively corrected one-dimensional topological quantum memories.

A SURVEY OF MODERN TECHNIQUES OF ERROR CORRECTION CODING

2021 ◽  
Author(s):  
П.В. ТРИФОНОВ ◽  
Б.Д. КУДРЯШОВ ◽  
В.Д. МИЛОСЛАВСКАЯ
Keyword(s):  
Error Correction ◽  
Storage Systems ◽  
Research Directions ◽  
Error Correction Coding ◽  
Decoding Algorithms ◽  
Code Constructions ◽  
And Storage

Рассмотрены методы помехоустойчивого кодирования, применяемые в современных системах передачи и хране -ния информации. Представлен краткий обзор кодовых конструкций, алгоритмов декодирования, достигаемыххарактеристик помехоустойчивости и производительности. Указаны основные достоинства и недостатки применяемых подходов, а также некоторые направления их развития. The paper discusses error correction coding techniques used in modern communication and storage systems. A brief survey of code constructions, decoding algorithms, and achievable performance and complexity is presented. The principal advantages and drawbacks of the considered techniques, as well as some further research directions, are outlined.

scholarly journals DESIGN OF CONFIGURABLE IP CORE FOR ERROR DETECTION AND CORRECTION

2014 ◽  
pp. 198-201
Author(s):  
AJILESH RK ◽  
ANAND K ◽  
NANDAKUMAR. R ◽  
SREEJEESH.S. G
Keyword(s):  
Intellectual Property ◽  
Error Correction ◽  
Error Detection ◽  
Word Length ◽  
Ip Core ◽  
Decoding Algorithms ◽  
Single Error ◽  
Error Detection And Correction

This paper addresses the design & implementation of configurable Intellectual Property (IP) core for double error detection and single error Correction. The encoding /decoding algorithms considered in this can be implemented with a simple and faster hardware. The block can be used for coding and decoding word having any length and correct single bit error occurred and detect double bit error, during transmission. The user can define the word length and the hamming bits required.

Research on Reed-Solomon Code in Complementary Code Keying Modulation Technology

2010 ◽  
Vol 44-47 ◽  
pp. 1070-1074
Author(s):  
Xi Su ◽  
Peng Bai ◽  
Yan Ping Feng ◽  
Yuan Yuan Wu
Keyword(s):  
Error Correction ◽  
System Performance ◽  
Error Probability ◽  
High Speed ◽  
High Signal ◽  
Decoding Algorithms ◽  
Coding Scheme ◽  
Reed Solomon Code ◽  
Simulation Results ◽  
Rs Coding

As the high speed expanding scheme adopted by IEEE802.11b standard, the Complementary Code Keying modulation technology can only perform well in error probability with high signal noise ratio. However, when SNR is comparably low or the number of users in the same channel augments suddenly, the system’s error probability soars. On the basis of the research on Complementary Code Keying, RS coding and decoding algorithms, this paper analyzed code parameters’ influence on error correction and accordingly promoted a coding scheme suitable for Complementary Code Keying: RS（255,239）. Simulation Results demonstrated that once SNR is upon 5.1dB the system performance would be greatly enhanced.

scholarly journals Design and Implementation of RS(450, 406) Decoder

2021 ◽  
Vol 12 (1) ◽  
pp. 19-43
Author(s):  
Akhilesh Yadav ◽  
Poonam Jindal ◽  
Devaraju Basappa
Keyword(s):  
Error Correction ◽  
Data Transmission ◽  
Channel Noise ◽  
Random Errors ◽  
Decoding Algorithms ◽  
Design And Implementation ◽  
Reed Solomon Code ◽  
Correction Technique ◽  
Functional Components ◽  
Efficient Decoding

Nowadays, in the field of data transmission between receiver and transmitter, the Reed Solomon code is used very frequently. FEC codes have two foremost and influential operations: (1) calculating parity symbols at the encoder side and (2) transmitting message symbols with parity symbols and decoding the received codeword at the second side by using the decoding algorithms. Gigabit automotive ethernet is used in the automotive car to provide better bandwidth for every kind of applications to connect functional components of the vehicles. This error correction technique is used in the gigabit automotive ethernet to reduce the channel noise during data transmission. RS (450, 406) is a powerful error correction techniques used in automotive ethernet. This paper focused only on the analysis of Reed Solomon decoding. Reed Solomon decoding is more efficient decoding techniques for correcting both burst and random errors. The critical steps of the Reed Solomon decoding are to solve the error evaluator and error calculator polynomial, which is also known as KES solver.

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