An Interpolation Algorithm using Gröbner Bases for Soft-Decision Decoding of Reed-Solomon Codes

Lee, Kwankyu; O’Sullivan, Michael E.

doi:10.1109/isit.2006.261906

Cited by 37 publications

(37 citation statements)

References 13 publications

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“…Then it is converted to a Gröbner basis, which can be defined equivalently as a basis whose polynomials have distinct y-degree in the leading terms [6].…”

Section: Algorithm A: Kötter's Interpolation Algorithmmentioning

confidence: 99%

“…in the corresponding module is subject to the constraint that it has the same common factor in f 0 (x). Hence, given the set of points to be passed, the Lagrange formula is adopted to calculate h(x) in [6]. However, the monic polynomial g(x) computed from the modified interpolation satisfies the same criteria, and can replace h(x).…”

Section: B Modified Basis Constructionmentioning

confidence: 99%

“…Although this can be done by the Kötter's algorithm, the polynomial evaluation needs to be carried out first. Alternatively, this paper proposes to use the monic polynomial directly in the construction of an initial basis, which is then converted to compute the polynomial with minimum weighted degree using the Lee-O'Sullivan (LO) [6] interpolation process. Our approach avoids not only the polynomial evaluation, but also the complicated computations for initial basis construction.…”

Section: Introductionmentioning

confidence: 99%

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On the implementation of modified fuzzy vault for biometric encryption

Zhang

Shi

Ritcey

2012

2012 Information Theory and Applications Workshop

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Abstract-Biometrics, such as irises and fingerprints, enable secure and non-repudiable authentication. Fuzzy vault is a scheme that can monolithically bind secret to biometric templates. Moreover, the modified fuzzy vault (MFV) leads to less entropy loss and requires less memory for storing the sketches. This paper proposes a novel low-complexity scheme to compute the monic polynomial for the sketch during the enrollment process of the MFV. An innovative interpolation method is also developed to reduce the computation complexity and latency of the verification process. Efficient hardware implementation architectures are developed in this paper for the proposed schemes and their complexities are analyzed in detail.

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“…Then it is converted to a Gröbner basis, which can be defined equivalently as a basis whose polynomials have distinct y-degree in the leading terms [6].…”

Section: Algorithm A: Kötter's Interpolation Algorithmmentioning

confidence: 99%

Section: B Modified Basis Constructionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the implementation of modified fuzzy vault for biometric encryption

Zhang

Shi

Ritcey

2012

2012 Information Theory and Applications Workshop

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“…In this paper, we focus on the interpolation step. Popular interpolation algorithms include the Nielson's algorithm and the Lee-O'Sullivan (LO) algorithm [13]. However, the LO algorithm can not take in more points once the interpolation started.…”

Section: The Bgmd Algorithm and The Nielson's Interpolationmentioning

confidence: 99%

Combined interpolation architecture for soft-decision decoding of Reed-Solomon codes

Zhu

Zhang

Wang

2008

2008 IEEE International Conference on Computer Design

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Abstract-Reed-Solomon (RS) codes are one of the most extensively used error control codes in digital communication and storage systems. Recently, significant advancements have been made on algebraic soft-decision decoding (ASD) of RS codes. These algorithms can achieve substantial coding gain with polynomial complexity. One major step of ASD is the interpolation. Various techniques have been proposed to reduce the complexity of this step. Further speedup of this step is limited by the inherent serial nature of the interpolation algorithm. In this paper, taking the bit-level generalized minimum distance (BGMD) ASD as an example, we propose a novel technique to combine the computations from multiple interpolation iterations. Compared to the single interpolation iteration architecture for a (255, 239) RS code, the combined architecture can achieve 2.7 times throughput with only 2% area overhead in high signal-to-noise ratio scenarios.

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“…RS 리스트 디코더를 위한 Interpolation 알고리즘으 로 Nielson [7] 과 Lee-O'Sullivan [8] 의 알고리즘이 있다. Interpolation은 매우 많은 반복 계산 과정을 포함하고 있어 레이턴시가 매우 큰데, 리인코딩(re-encoding) 기 법을 사용하여 반복 계산과정을 알고리즘 차원에서 줄 일 수 있다 [9] .…”

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Area-efficient Interpolation Architecture for Soft-Decision List Decoding of Reed-Solomon Codes

Lee¹,

Park²

2013

Journal of the Institute of Electronics Engineers of Korea

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Reed-Solomon (RS) codes are powerful error-correcting codes used in diverse applications. Recently, algebraic soft-decision decoding algorithm for RS codes that can correct the errors beyond the error correcting bound has been proposed. The algorithm requires very intensive computations for interpolation, therefore an efficient VLSI architecture, which is realizable in hardware with a moderate hardware complexity, is mandatory for various applications. In this paper, we propose an efficient architecture with low hardware complexity for interpolation in soft-decision list decoding of Reed-Solomon codes. The proposed architecture processes the candidate polynomial in such a way that the terms of X degrees are processed in serial and the terms of Y degrees are processed in parallel. The processing order of candidate polynomials adaptively changes to increase the efficiency of memory access for coefficients; this minimizes the internal registers and the number of memory accesses and simplifies the memory structure by combining and storing data in memory. Also, the proposed architecture shows high hardware efficiency, since each module is balanced in terms of latency and the modules are maximally overlapped in schedule. The proposed interpolation architecture for the (255, 239) RS list decoder is designed and synthesized using the DongbuHitek 0.18 standard cell library, the number of gate counts is 25.1K and the maximum operating frequency is 200 MHz.

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An Interpolation Algorithm using Gröbner Bases for Soft-Decision Decoding of Reed-Solomon Codes

Cited by 37 publications

References 13 publications

On the implementation of modified fuzzy vault for biometric encryption

On the implementation of modified fuzzy vault for biometric encryption

Combined interpolation architecture for soft-decision decoding of Reed-Solomon codes

Area-efficient Interpolation Architecture for Soft-Decision List Decoding of Reed-Solomon Codes

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