Performance of Reed–Solomon codes using the Guruswami–Sudan algorithm with improved interpolation efficiency (original) (raw)
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INTERNATIONAL JOURNAL OF ENGINEERING DEVELOPMENT AND RESEARCH (IJEDR) (ISSN:2321-9939), 2014
Reed-Solomon codes are very useful and effective in burst error in noisy environment. In decoding process for 1 error or 2 errors create easily with using procedure of Peterson-Gorenstein –Zierler algorithm. If decoding process for 3 or more errors, these errors can be solved with key equation of a new algorithm named Berlekamp-massey algorithm. In this paper, wide discussion of procedures of Peterson-Gorenstein –Zierler algorithm and Berlekamp-Massey algorithm and show the advantages of modified version of Berlekam-Massey algorithm with its steps.
A Simplified Step-by-Step Decoding Algorithm for Parallel Decoding of Reed-Solomon Codes
IEEE Transactions on Communications, 2007
A simplified parallel step-by-step decoding algorithm is proposed for decoding Reed-Solomon (RS) codes. It uses new method to calculate the determinants of the temporarily changed syndrome matrices, based on the property of these matrices determined in this paper. By using the proposed method, the calculations of the determinants of the temporarily changed syndrome matrices become much simpler and thus the computational complexity of the step-by-step decoding algorithm is significantly reduced.
A Simplified Step-by-Step Decoding Algorithm for Parallel Decoding of Reed–Solomon Codes
IEEE Transactions on Communications, 2000
A simplified parallel step-by-step decoding algorithm is proposed for decoding Reed-Solomon (RS) codes. It uses new method to calculate the determinants of the temporarily changed syndrome matrices, based on the property of these matrices determined in this paper. By using the proposed method, the calculations of the determinants of the temporarily changed syndrome matrices become much simpler and thus the computational complexity of the step-by-step decoding algorithm is significantly reduced.
A Hybrid Decoding Method for Short-Blocklength Reed Solomon Codes
The standard Berlekamp-Massey iterative algorithm, although the most commonly used decoding method for Reed-Solomon (RS) codes, is computationally complex. A novel decoding technique that combines error trapping decoding and the Berlekamp-Massey algorithm is proposed in this article. It is demonstrated that this decoder maintains the simplicity of the error trapping decoder for the most part. Moreover, it is shown that whenever it is necessary to apply the maximum error correcting capability of the code, only a shortened Berlekamp-Massey algorithm is utilized. Substantial improvement in the decoder throughput relative to that of Berlekamp-Massey decoding is reported. Software simulation is used to verify the theoretical performance analysis.
Two new decoding algorithms for Reed-Solomon codes
Applicable Algebra in Engineering, Communication and Computing, 1994
The subject of decoding Reed-Solomon codes is considered, By reformulating the Berlekamp and Welch key equation and introducing new versions of this key equation, two new decoding algorithms for Reed-Solomon codes will be presented. The two new decoding algorithms are significant for three reasons. Firstly the new equations and algorithms represent a novel approach to the extensively researched problem of decoding Reed-Solomon codes. Secondly the algorithms have algorithmic and implementation complexity comparable to existing decoding algorithms, and as such present a viable solution for decoding Reed-Solomon codes. Thirdly the new ideas presented suggest a direction for future research. The first algorithm uses the extended Euclidean algorithm an~t is very efficient for a systolic VLSI implementation. The second decoding algorithm presented is similar in nature to the original decoding algorithm of Peterson except that the syndromes do not need to be computed and the remainders are used directly. It has a regular structure and will be efficient for implementation only for correcting a small number of errors. A systolic design for computing the Lagrange interpolation of a polynomial, which is needed for the first decoding algorithm, is also presented.
Iterative algebraic soft-decision list decoding of Reed-Solomon codes
IEEE Journal on Selected Areas in Communications, 2006
In this paper, we present an iterative soft-decision decoding algorithm for Reed-Solomon (RS) codes offering both complexity and performance advantages over previously known decoding algorithms. Our algorithm is a list decoding algorithm which combines two powerful soft-decision decoding techniques which were previously regarded in the literature as competitive, namely, the Koetter-Vardy algebraic soft-decision decoding algorithm and belief-propagation based on adaptive parity-check matrices, recently proposed by Jiang and Narayanan. Building on the Jiang-Narayanan algorithm, we present a belief-propagation-based algorithm with a significant reduction in computational complexity. We introduce the concept of using a belief-propagation-based decoder to enhance the soft-input information prior to decoding with an algebraic soft-decision decoder. Our algorithm can also be viewed as an interpolation multiplicity assignment scheme for algebraic soft-decision decoding of RS codes.
Iterative Decoding of Reed-Solomon Codes based on Non-binary Matrices
2019 IEEE International Symposium on Information Theory (ISIT), 2019
A novel iterative approach for soft-decision decoding of Reed-Solomon codes is presented that employs symbol-level belief propagation on an alternative parity-check matrix representation of the code. Construction of a suitable matrix is discussed from the viewpoint of iterative decoding, and certain conditions are derived on existence of structures detrimental for decoding. Simulation results demonstrate that the novel scheme performs substantially better than hard-decision decoding, especially with high rate codes, while being of much lower complexity than existing soft-decision decoding methods. Proposed method is also well-suited for efficient hardware implementations.
Efficient Low-Complexity Decoding of CCSDS Reed Solomon Codes Based on Justesen’s Concatenation
IEEE Access
Forward error correction (FEC) is a key capability in modern satellite communications that provides the system designer with the needed flexibility to comply with the different applications' requirements. Reed-Solomon codes are well known for their ability to optimize between the system power, bandwidth, data rate and quality of service. This paper introduces an efficient decoding scheme for decoding the Reed-Solomon (RS) codes adhering to the Consultative Committee for Space Data Systems (CCSDS) standards based on Justesen's construction of concatenation. To maintain the standard output size, the proposed scheme first encodes every m-1 bits using the single-parity-check (SPC) code, while the Reed-Solomon code encodes K SPC codewords into N symbols that are of the same size as CCSDS standard. Decoding on the inner SPC code is based on Maximum-Likelihood decoding Kaneko algorithm, while for the proposed coding scheme the reduced test-pattern Chase algorithm is adopted for decoding the outer RS code. Simulation results show coding gains of 1.4 dB and 7 dB compared with the algebraic decoding of RS codes over AWGN and Rayleigh fading channels, respectively. Moreover, the adopted reduced test-pattern Chase algorithm for decoding RS code achieves an overall complexity reduction of 40% compared to conventional Chase decoding algorithm. INDEX TERMS CCSDS, Chase algorithm, concatenated codes, Justesen code, Reed-Solomon code, and Single-Parity-Check.