Blind Recognition of RS Codes Based on Galois Field Fourier Transform

2016 ◽  
Author(s):  
Xiaokai Zhang ◽  
Gang Wu ◽  
Bangning Zhang ◽  
Daoxing Guo ◽  
Kefeng Guo
Keyword(s):  
Fourier Transform ◽  
Galois Field ◽  
Rs Codes ◽  
Blind Recognition

Multiplier-Free Implementation of Galois Field Fourier Transform on a FPGA

2019 ◽  
Vol 66 (11) ◽  
pp. 1815-1819
Author(s):  
Sree Balaji Girisankar ◽  
Mona Nasseri ◽  
Jennifer Priscilla ◽  
Shu Lin ◽  
Venkatesh Akella
Keyword(s):  
Fourier Transform ◽  
Galois Field

Blind Recognition of Reed-Solomon Codes Based on Histogram Statistic of Galois Field Spectra

2013 ◽  
Vol 791-793 ◽  
pp. 2088-2091
Author(s):  
Hui Xie ◽  
Feng Hua Wang ◽  
Zhi Tao Huang
Keyword(s):  
Reverse Engineering ◽  
Error Rate ◽  
Communication System ◽  
Spectral Characteristics ◽  
Galois Field ◽  
Probability Of Detection ◽  
Noisy Environment ◽  
Engineering Communication ◽  
Rs Code ◽  
Blind Recognition

We focus on the recognition of RS code in a reverse-engineering communication system, and an algorithm based on spectral statistic is proposed, which makes use of the spectral characteristics of RS code. When there are some codes with errors in the observations, the spectral histogram statistic is computed, which can improve the probability of detection in the noisy environment. Experimental results are given to illustrate the performances of the method which can get a 90% probability of detection of (255, 223) RS code in the presence of 0.5% code error rate.

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 A New Minimize Matrix Computation Coding Method for Distributed Storage Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Chao Yin ◽  
Haitao Lv ◽  
Tongfang Li ◽  
Xiaoping Qu ◽  
Jianzong Wang ◽  
...  
Keyword(s):  
Storage Systems ◽  
Distributed Storage ◽  
Galois Field ◽  
Storage Space ◽  
Matrix Computation ◽  
Rs Codes ◽  
Failure Tolerance ◽  
Xor Operation ◽  
The Matrix ◽  
Distributed Storage Systems

With the number of nodes increasing in scale, the requirements of storage space enlarge sharply in distributed storage systems. Failure-tolerance schemes such as Reed–Solomon codes (RS codes in short) and Cauchy Reed–Solomon codes (CRS codes in short) are used to save storage space. However, these failure-tolerance schemes severely degrade the system performance. In this paper, we propose optimal RS codes (OptRS codes in short) based on RS codes and CRS codes that can offer better performance for encoding and decoding as well as maximizing the utilization of storage space. OptRS codes can speed up the matrix computation which is regarded as the most important factor to impact the efficiency of coding by transferring the matrix computation from the Galois field mapping to the XOR operation. OptRS codes employ an algorithm called row elimination scheme (RE scheme in short), which can eliminate the same XOR operation to minimize the number of XOR operations. We analyze optimal matrices (OM in short) in theory, which prove the optimal performance of OptRS codes over the Galois field. Our method is implemented on the top of the distributed storage system, and code parameters were carefully chosen. The test result shows that OptRS codes can improve the performance in different data block numbers, parity block numbers, block size, normal reading, and degraded reading, compared with RS codes and CRS codes.

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