A stamping technique to increase the error correction capacity of the (127,k,d) RS code

2002 ◽  
Author(s):  
T. Vallino ◽  
A. Dandache ◽  
F. Monteiro ◽  
B. Lepley ◽  
J.P. Delahaye
Keyword(s):  
Error Correction ◽  
Rs Code

Error Recovery System Encoder/Decoder Method and VHDL Design for Saving Memory of Embedded System

2011 ◽  
Vol 110-116 ◽  
pp. 4985-4991
Author(s):  
Byung Joon Kim ◽  
Rae Cho Sung ◽  
Sung Ho Jin
Keyword(s):  
Embedded System ◽  
Error Correction ◽  
Recovery Process ◽  
Error Recovery ◽  
Correction Method ◽  
Memory Space ◽  
Rs Code ◽  
Error Correction Method ◽  
Recovery System ◽  
System Errors

Unexpected errors may occur in any embedded systems. An error correction circuitry is used to prevent system errors. Parity bits generated from an encoder are needed to perform an error recovery process. Therefore, to be stored in the memory space should be added. In this paper, Parity bits to be stored without a memory space that can be used to error correction circuitry are proposed. The proposed method was designed in VHDL. The proposed design used the Reed-Solomon (RS) code of an error correction method. Then, 8 bits of information symbols and a symbol error correcting RS code were designed based on the design.

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.

scholarly journals Forward Error Correction For Gigabit Automotive Ethernet using RS(450,406) Encoder

2019 ◽  
Vol 9 (2S) ◽  
pp. 117-123
Keyword(s):  
Error Correction ◽  
Data Transmission ◽  
Communication System ◽  
Forward Error Correction ◽  
Rs Codes ◽  
Reed Solomon Codes ◽  
Rs Code ◽  
Correction Technique ◽  
Forward Error ◽  
Rs Coding

Error correction and detection during data transmission is a major issue. For resolving this, many error correction techniques are available. The Reed-Solomon coding is the most powerful forward error correction technique used in Gigabit Automotive Ethernet to compact channel noise during data transmission. The car becomes more smarter day by day and more new advanced electronics is being used in-vehicle. Gigabit Automotive Ethernet(1000BASE-T1) provide fast bandwidth for many kinds of applications and connect different functional parts in the car. The Reed Solomon(RS) coding is the powerful forward error correction(FEC) technique used in 1000BASE-T1 Automotive Ethernet. RS(450,406) coding is also known as shortened Reed Solomon codes. The Reed Solomon(RS) codes are generally used in communication system due to its ability of correcting both random and burst errors. Reed Solomon codes are no-binary systematic linear block codes. RS coding is widely used in high speed communication system. This RS code is implemented using Galois field(GF). The Automotive Ethernet is encoded using RS(450,406) codes through GF(512) for FEC. This RS codes can corrects the error up to t=22 symbol, while other encoding techniques corrects the error in t bits. In this paper we implemented the RS(Reed Solomon) code in Cadence ncsim Verilog software and used Cadence Simvision for showing timing diagrams. This RS code uses 9-bit based shortened (450,406) code.

scholarly journals Performance Investigation of MIMO Based CO-OFDM FSO Communication Link for BPSK, QPSK and 16-QAM under the Influence of Reed Solomon Codes

2021 ◽  
Vol 53 (5) ◽  
pp. 210508
Author(s):  
Suresh Kumar ◽  
Payal Payal
Keyword(s):  
Error Correction ◽  
Signal To Noise Ratio ◽  
Communication Link ◽  
Link Length ◽  
Link Distance ◽  
Rs Code ◽  
Error Correction Capability ◽  
Wide Scale ◽  
Propagation Medium ◽  
Novel Concept

The MIMO based CO-OFDM FSO communication system is emerging as a promising approach to meet the future bandwidth requirements for seamless communication. The atmosphere being the propagation medium is a major hindrance in wide-scale acceptability of FSO technology. For seamless and error-free transmission and reception of data, a novel concept of MIMO integrated with RS code is proposed in this paper. The system performance of an RS 64 (RS (255,127)) coded MIMO-based CO-OFDM FSO communication link was investigated using BPSK, QPSK and 16-QAM under the combined effects of geometric losses, path losses and atmospheric attenuations at a hitherto un-investigated data rate of 40 Gbps and a link distance of 5 km. The modified gamma-gamma distribution was used for modeling a moderately turbulent channel. With link length varying over a range of 1 to 5 km, error correction was maximum in 16-QAM as compared to BPSK and QPSK, with 150 to 167 corrected errors. In terms of PAPR, PSK was more apt than QAM, but with a compromise in BER. The geometric losses were reduced with link length due to an increase in error correction capability for all three modulation cases, with the least losses occurring in 16-QAM. At the target bit error rate (BER), the signal to noise ratio (SNR) required for BPSK and QPSK was higher by 3.98 dB and 6.14 dB compared to 16-QAM.

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