Fast Chase Decoding Algorithms and Architectures for Reed–Solomon Codes

Wu, Yingquan

doi:10.1109/tit.2011.2165524

Cited by 25 publications

(40 citation statements)

References 20 publications

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“…To share computations among the decoding trials, one-pass schemes were proposed for BCH codes [1], [2]. They adopt the Berlekamp's algorithm to compute the error locator of the first test vector.…”

Section: Introductionmentioning

confidence: 99%

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Interpolation-based Chase BCH decoder

Zhang

2014

2014 Information Theory and Applications Workshop (ITA)

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Abstract-BCH codes are adopted in many applications, such as flash memory and optical communications. Compared to harddecision decoders, the soft-decision Chase BCH decoder can achieve significant coding gain by trying multiple test vectors. Previously, one-pass Chase BCH decoding schemes based on the Berlekamp's algorithm are used to share intermediate results among the decoding trials. In this paper, it will be shown that the interpolation-based one-pass Chase BCH decoder has much lower hardware complexity. Techniques for simplifying the implementation architecture for each step of the interpolationbased decoder are summarized. For a (4200, 4096) BCH code, the interpolation-based Chase decoder with 16 test vectors has 2.2 times higher hardware efficiency than that based on the Berlekamp's algorithm in terms of throughput-over-area ratio.

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Section: Introductionmentioning

confidence: 99%

“…Then the locators of the other vectors are derived in one run by updating the results of the Berlekamp's algorithm. The scheme in [2] was further simplified and implementation architectures were designed in [3]. Nevertheless, the Chase BCH decoding can be more efficiently implemented using an interpolation-based scheme [4].…”

Section: Introductionmentioning

confidence: 99%

Interpolation-based Chase BCH decoder

Zhang

2014

2014 Information Theory and Applications Workshop (ITA)

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“…The low-complexity VLSI architectures for soft decoders have been developed in recent years [9], [11]- [14]. However, these soft decoders still require several times area than the hard decoders does and practical implementations have not been applied.…”

Section: Introductionmentioning

confidence: 99%

A 2.56 Gb/s soft RS (255,239) decoder chip for optical communication systems

Hsu

Lin

Chang

et al. 2011

2011 Proceedings of the ESSCIRC (ESSCIRC)

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Abstract-Due to high transmission rate requirement for optical communication systems, the growing uncertainty of received signals results in the limited transmission distance. In this paper, a decision-confined soft RS decoder chip is proposed to enhance the error correcting performance with area-efficient architectures. Instead of generating numerous possible candidate codewords and determining the most likely one as output codeword, our approach produces only one codeword by confining the degree of error location polynomial. Therefore, hardware complexity is significantly reduced by eliminating decision making unit. Moreover, an iteration-reduced RiBM algorithm is provided to enlarge the coding gain by using more least reliable positions (LRPs) in the limited operation latency. According to simulation results, our proposed soft RS (255, 239; 8) decoder with 5 LRPs outperforms 0.4 dB at codeword error rate (CER) as compared to hard RS decoders. Implemented in standard CMOS 90 nm technology, the soft decoder chip can achieve 2.56 Gb/s throughput with similar complexity as a hard decoder. It can fit well for 10-40 Gb/s with 16 RS decoders in optical fiber systems and 2.5 Gb/s GPON applications.

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“…Bellorado et al [14] presented a Chase-type interpolation, which exploits the similarity among test vectors to obtain the set of candidate codewords; thereby reducing the interpolation complexity. Wu [15] developed a one-pass Chase algorithm for decoding RS codes, which has a complexity of O(dn 2 ), where d is the minimum distance. In [15], the corresponding VLSI architecture was also designed.…”

mentioning

confidence: 99%

“…Wu [15] developed a one-pass Chase algorithm for decoding RS codes, which has a complexity of O(dn 2 ), where d is the minimum distance. In [15], the corresponding VLSI architecture was also designed. Chen et al [17] proposed a progressive algebraic soft-decision (ASD) decoding algorithm in which the factorization output list size is enlarged progressively.…”

mentioning

confidence: 99%

On Soft-Information-Based Error and Erasure Decoding of Reed–Solomon Codes in Burst Rayleigh Fading Channels

Huang

et al. 2019

IEEE Trans. Commun.

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In this paper, two new decoding algorithms to decode Reed-Solomon (RS) codes during transmission over burst Rayleigh fading channels with additive white Gaussian noise (AWGN) are proposed. They only conduct error correction for coded symbols located in the pure AWGN region, and conduct error and erasure correction for those symbols located in the burst fading region by treating those coded symbols that are very likely erroneous as erasures. The first algorithm does not need to know the fading locations in advance, while the second algorithm assumes that the fading locations are known. In addition, the performance of such two algorithms is studied when a precomputed threshold is used to determine the erasures of the code. Simulation results show that our proposed algorithms not only significantly perform better than the classic Berlekamp-Messay (BM) algorithm with a comparable computational complexity, but also achieve a better trade-off between the performance and the computational complexity when compared with other existing algorithms. In particular, our algorithms exhibit excellent robustness for tested various code parameters and fading configurations. Furthermore, a more detailed mathematical analysis is also developed in this paper in order to estimate the performance of the new algorithms in the burst Rayleigh fading channels. We observe that the performance of the first algorithm can only be estimated relatively accurately when encountering burst deep-fading, whereas the performance prediction for the second algorithm is always in agreement with the simulation results for various fading cases.

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Fast Chase Decoding Algorithms and Architectures for Reed–Solomon Codes

Cited by 25 publications

References 20 publications

Interpolation-based Chase BCH decoder

Interpolation-based Chase BCH decoder

A 2.56 Gb/s soft RS (255,239) decoder chip for optical communication systems

On Soft-Information-Based Error and Erasure Decoding of Reed–Solomon Codes in Burst Rayleigh Fading Channels

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