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

Truong, Trieu‐Kien; Jeng, Jyh-Horng; Cheng, Taikun

doi:10.1109/tcomm.2003.809764

Cited by 25 publications

(36 citation statements)

References 14 publications

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“…This section gives a brief review of RS decoding and summarizes the TME algorithm presented in [2], which forms the basis of this work.…”

Section: Background and Notationmentioning

confidence: 99%

“…The proposed architecture is based on the TME algorithm [2]. For completeness, the TME algorithm is briefly reviewed below.…”

Section: Tme Algorithmmentioning

confidence: 99%

“…Together with the control mechanism of u 0 and 2l ≤ k in (10), the TME algorithm removes the need for the degree computation and comparison in conventional ME algorithms [1]. After 2t iterations, the desired Ω (b) (x) and Λ (b) (x) are obtained simultaneously, and the results can be directly used in the Chien search and the Forney algorithm for finding the error locators and the error values [2].…”

Section: Tme2mentioning

confidence: 99%

“…Figure 6 shows the timing relationship among the three units of the decoder. Compared with the architectures derived based on the conventional ME [1] or the TME [2] algorithms, the idle time of the developed KES unit is greatly reduced from 239 to 31 clock cycles. This means that the hardware utilization of the proposed decoder is improved by the pipelining strategy.…”

Section: Csee Unitmentioning

confidence: 99%

“…Compared with the BM algorithm, the ME algorithm usually leads to a more regular architecture with a higher computational complexity and hardware requirement. Recently, Truong et al presented a fast ME algorithm [2], denoted as the TME algorithm hereafter, which greatly reduces complexity by eliminating the need for degree computation and comparison.…”

Section: Introductionmentioning

confidence: 99%

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Design and Implementation of a Low-Complexity Reed-Solomon Decoder for Optical Communication Systems

Shieh

2011

IEICE Trans. Inf. & Syst.

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SUMMARYA low-complexity Reed-Solomon (RS) decoder design based on the modified Euclidean (ME) algorithm proposed by Truong is presented in this paper. Low complexity is achieved by reformulating Truong's ME algorithm using the proposed polynomial manipulation scheme so that a more compact polynomial representation can be derived. Together with the developed folding scheme and simplified boundary cell, the resulting design effectively reduces the hardware complexity while meeting the throughput requirements of optical communication systems. Experimental results demonstrate that the developed RS(255, 239) decoder, implemented in the TSMC 0.18 μm process, can operate at up to 425 MHz and achieve a throughput rate of 3.4 Gbps with a total gate count of 11,759. Compared to related works, the proposed decoder has the lowest area requirement and the smallest area-time complexity.

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“…This section gives a brief review of RS decoding and summarizes the TME algorithm presented in [2], which forms the basis of this work.…”

Section: Background and Notationmentioning

confidence: 99%

“…The proposed architecture is based on the TME algorithm [2]. For completeness, the TME algorithm is briefly reviewed below.…”

Section: Tme Algorithmmentioning

confidence: 99%

Section: Tme2mentioning

confidence: 99%

Section: Csee Unitmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Design and Implementation of a Low-Complexity Reed-Solomon Decoder for Optical Communication Systems

Shieh

2011

IEICE Trans. Inf. & Syst.

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A Kind of Design for CCSDS Standard GF(28) Multiplier

Zhang¹,

Dong²,

Zhang³

et al. 2021

Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

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Method for correcting both errors and erasures of RS codes using error‐only and erasure‐only decoding algorithms

Lu¹,

Lu²,

Chen

2013

Electron. lett.

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A method for correcting both errors and erasures of Reed-Solomon (RS) codes using error-only and erasure-only decoding algorithms is proposed. First, the method removes the effect of erasures from syndromes, then it uses error-only and erasure-only correcting processes to correct errors and erasures, respectively; thus, the overall decoding complexity can be reduced substantially. Furthermore, with hardware implementation, the most time-consuming operations in these two processes can be calculated concurrently to obtain a significant reduction of decoding latency.Introduction: Reed-Solomon (RS) codes form a class of powerful random-error and multiple burst-error correcting codes such that they have been widely used in data communications and storage systems. Since (n, k) RS codes have the largest possible minimum distance d min = n − k + 1, the codes are classified as the class of maximum-distance-separable codes [1,2]. It is well-known that a code, with the minimum distance d min , has the capability of correcting all combinations of v symbol errors and e symbol erasures on the condition of 2v + e ≤ d min -1 [1-4], therefore three types of decoding algorithms can be derived: (i) for error-only correcting, (ii) for errorand-erasure correcting, and (iii) for erasure-only correcting. Among them, the erasure-only decoding type algorithms are the simplest and fastest because all erasure locations have been known. On the other hand, the error-and-erasure correcting type algorithms may be the most complicated and time-consuming because their syndrome polynomial, error-/erasure-location polynomial and error-/erasure-value evaluator have higher degrees than the error-only correcting type algorithms [5].For correcting both errors and erasures of RS codes, several wellknown methods can be found from [1][2][3][4]. In this Letter, we divide the error-and-erasure decoding procedure into two processes: (i) erroronly correcting and (ii) erasure-only correcting processes. The main operations in the error-only correcting process are to remove the effect of erasures from syndromes, as well as to find error locations and error values. The complexity of the error-only correcting process is less than that of the error-and-erasure correcting process because the effect of erasures has been removed, particularly for e≫v. The erasure-only correcting process corrects erasures using the modified syndromes which are refined from the original syndromes by removing the effect of errors. Since a complicated error-and-erasure correcting procedure has been divided into two simpler correcting processes, the overall decoding complexity can be reduced substantially. In addition, the most time-consuming operations in the erasure-only and error-only correcting processes can be computed concurrently by hardware circuits, so that the decoding delay will be efficiently reduced.

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

Cited by 25 publications

References 14 publications

Design and Implementation of a Low-Complexity Reed-Solomon Decoder for Optical Communication Systems

Design and Implementation of a Low-Complexity Reed-Solomon Decoder for Optical Communication Systems

A Kind of Design for CCSDS Standard GF(28) Multiplier

Method for correcting both errors and erasures of RS codes using error‐only and erasure‐only decoding algorithms

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