Decoding generalized concatenated codes using Interleaved Reed-Solomon codes (original) (raw)

Collaborative Decoding of Interleaved Reed–Solomon Codes and Concatenated Code Designs

IEEE Transactions on Information Theory, 2000

Interleaved Reed-Solomon codes are applied in numerous data processing, data transmission, and data storage systems. They are generated by interleaving several codewords of ordinary Reed-Solomon codes. Usually, these codewords are decoded independently by classical algebraic decoding methods. However, by collaborative algebraic decoding approaches, such interleaved schemes allow the correction of error patterns beyond half the minimum distance, provided that the errors in the received signal occur in bursts. In this work, collaborative decoding of interleaved Reed-Solomon codes by multi-sequence shift-register synthesis is considered and analyzed. Based on the framework of interleaved Reed-Solomon codes, concatenated code designs are investigated, which are obtained by interleaving several Reed-Solomon codes, and concatenating them with an inner block code.

Decoding interleaved Reed–Solomon codes beyond their joint error-correcting capability

Designs, Codes and Cryptography, 2012

A new lower bound on the minimum distance of qary cyclic codes is proposed. This bound improves upon the Bose-Chaudhuri-Hocquenghem (BCH) bound and, for some codes, upon the Hartmann-Tzeng (HT) bound. Several Boston bounds are special cases of our bound. For some classes of codes the bound on the minimum distance is refined. Furthermore, a quadratic-time decoding algorithm up to this new bound is developed. The determination of the error locations is based on the Euclidean Algorithm and a modified Chien search. The error evaluation is done by solving a generalization of Forney's formula.

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.

Unambiguous Decoding of Generalized Reed–Solomon Codes Beyond Half the Minimum Distance

2010

The Schmidt–Sidorenko–Bossert scheme extends a low-rate Reed–Solomon code to an Interleaved Reed–Solomon code and achieves the decoding radius of Sudan’s original list decoding algorithm while the decoding result remains unambiguous. We adapt this result to the case of Generalized Reed–Solomon codes and calculate the parameters of the corresponding Interleaved Generalized Reed–Solomon code. Furthermore, the failure probability is derived.

Erasure decoding of five times extended Reed-Solomon codes

Journal of Electrical Engineering, 2019

Recently a new family of error control codes was proposed which are equivalent to five times extended Reed-Solomon codes. In this paper an erasure decoding algorithm for these codes is proposed.

Analysis of bounded distance decoding for reed Solomon codes

2018

Masters Report A report submitted in ful llment of the requirements for the degree of Master of Science (50/50) in the Centre for Telecommunication Access and Services (CeTAS) School of Electrical and Information Engineering Faculty of Engineering and the Built Environment February 2017

A new decoding algorithm for correcting both erasures and errors of reed-solomon codes

IEEE Transactions on Communications, 2003

In this paper, a high efficient decoding algorithm is developed here in order to correct both erasures and errors for Reed-Solomon (RS) codes based on the Euclidean algorithm together with the Berlekamp-Massey (BM) algorithm. The new decoding algorithm computes the errata locator polynomial and the errata evaluator polynomial simultaneously without performing polynomial divisions, and there is no need for the computation of the discrepancies and the field element inversions. Also, the separate computation of the Forney syndrome needed in the decoder is completely avoided. As a consequence, the complexity of this new decoding algorithm is dramatically reduced. Finally, the new algorithm has been verified through a software simulation using C ++ language. An illustrative example of (255,239) RS code using this program shows that the speed of the decoding process is approximately three times faster than that of the inverse-free Berlekamp-Massey algorithm.

Performance of Reed–Solomon codes in concatenated schemes with nonideal interleaving

European Transactions on Telecommunications, 2007

The prediction of the performance of a Reed-Solomon (RS) code has an analytical solution in case of statistical independence of the errors at the input of the RS decoder (RSD). In concatenated schemes, this condition is often obtained through an interleaving device disrupting the correlation between erroneous symbols. Sometimes the ideal depth of such interleaver is too large to implement and the RSD must operate in sub-optimal conditions, for which no analytical formulas are available. In this paper, we propose a statistical model that can manage under-dimensioned interleavers. With a mild set of hypotheses on the behaviour of the inner decoder (ID), we derive analytical expressions for the performance of the concatenated code. Input data for the model can be analytical or can be obtained by simulation. We apply the method to two different types of inner codes, namely turbo codes and RS codes, and we compare the results predicted by the model with those obtained through simulation, when available, showing a very good agreement. Figure 3. Histogram (a) of byte error positions at the turbo decoder output and correlation coefficient (b) for n = 128 (E b /N 0 = 4.45 dB).

New Approaches to the Analysis and Design of Reed-Solomon Related Codes

2007

The research that led to this thesis was inspired by Sudan's breakthrough that demonstrated that Reed-Solomon codes can correct more errors than previously thought. This breakthrough can render the current state-of-the-art Reed-Solomon decoders obsolete. Much of the importance of Reed-Solomon codes stems from their ubiquity and utility. This thesis takes a few steps toward a deeper understanding of Reed-Solomon codes as well as toward the design of efficient algorithms for decoding them. After studying the binary images of Reed-Solomon codes, we proceeded to analyze their performance under optimum decoding. Moreover, we investigated the performance of Reed-Solomon codes in network scenarios when the code is shared by many users or applications. We proved that Reed-Solomon codes have many more desirable properties. Algebraic soft decoding of Reed-Solomon codes is a class of algorithms that was stirred by Sudan's breakthrough. We developed a mathematical model for algebraic so...