Reliability-Based Forward Recursive Algorithms for Algebraic Soft-Decision Decoding of Reed--Solomon Codes

Xia, Haitao; Cruz, J.R.

doi:10.1109/tcomm.2007.900539

Cited by 9 publications

(16 citation statements)

References 23 publications

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“…The final output bivariate polynomial , is selected from the polynomials in vector as the one with the smallest weighted degree. It is worth noting that the order of multiplication of the vectors can be changed arbitrarily, and that reliability information can be used to select a specific order to improve the performance of the algorithm [6]. In addition, the interpolation of a given point can be reversed recursively since .…”

Section: Interpolation-based Rs Decoding Algorithms and Their Recmentioning

confidence: 99%

“…The polynomial interpolation is the most computational complex step, and the common feature of these two algorithms and of a host of related ones which we will refer to as interpolation-based algorithms. The focus of most of the recent work on interpolation-based algorithms has been on improving their performance and reducing their computational complexity [3]- [7]. For example, in [3], a Chase-type algorithm with improved performance was introduced, and in [4], Gross et al used a re-encoding technique to reduce the complexity of the interpolation step.…”

Section: Introductionmentioning

confidence: 99%

“…Bellorado and Kavcic [5] presented a low complexity algorithm utilizing both the re-encoding technique and a Chase algorithm, and using a constant multiplicity of one. Forward generalized minimum distance (GMD)-type and recursive Chase algorithms were proposed in [6], [7].…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we further investigate the recursive property of the interpolation-based RS decoding algorithms originally presented in [6], and propose an efficient recursive algorithm for algebraic soft-decision decoding of RS Chase [8] and GMD [9] concepts to achieve short latency as well as improved decoding performance by further exploiting the channel reliability information. The paper is organized as follows: In Section II, we present a brief summary of interpolation-based algorithms and discuss their recursive property, and in Section III we investigate the decoding performance of the reliability-based recursive algorithms.…”

Section: Introductionmentioning

confidence: 99%

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A Chase-GMD Algorithm for Soft-Decision Decoding of Reed-Solomon Codes on Perpendicular Recording Channels

Xia¹,

Wang

Cruz

2008

2008 IEEE International Conference on Communications

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We propose a soft-decision Reed-Solomon (RS) decoding algorithm, which uses the combined approaches of the Chase and the generalized minimum distance (GMD) algorithms and exploits the recursive property of interpolation-based RS decoding algorithms. We evaluate the performance of this Chase-GMD type algorithm on perpendicular magnetic recording systems, and present simulation results that show that we can achieve better performance with fairly short latency and lower decoding complexity than the current state-of-art algorithms. Index Terms-Chase algorithm, generalized minimum distance algorithm,Guruswami-Sudan algorithm, Koetter-Vardy algorithm, list decoding, perpendicular magnetic recording channels, polynomial interpolation, Reed-Solomon codes, reliability-based decoding, soft-decision decoding.

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Section: Interpolation-based Rs Decoding Algorithms and Their Recmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Chase-GMD Algorithm for Soft-Decision Decoding of Reed-Solomon Codes on Perpendicular Recording Channels

Xia¹,

Wang

Cruz

2008

2008 IEEE International Conference on Communications

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“…In [9], it was mentioned that the interpolation-based decoding algorithm can be viewed as a GMD decoding. However, the hardware implementation issues of the interpolation-based one-pass GMD decoding are not considered.…”

Section: Introductionmentioning

confidence: 99%

Efficient Generalized Minimum-distance Decoders of Reed-Solomon Codes

Zhu

Zhang

2011

J Sign Process Syst

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Generalized minimum distance (GMD) decoding of Reed-Solomon (RS) codes can correct more errors than conventional hard-decision decoding by running error-and-erasure decoding multiple times for different erasure patterns. The latency of the GMD decoding can be reduced by the Kötter's one-pass decoding scheme. This scheme first carries out an erroronly hard-decision decoding. Then all pairs of errorerasure locators and evaluators are derived iteratively in one run based on the result of the error-only decoding. In this paper, a more efficient interpolation-based one-pass GMD decoding scheme is studied. Applying the re-encoding and coordinate transformation, the result of erasure-only decoding can be directly derived. Then the locator and evaluator pairs for other erasure patterns are generated iteratively by applying interpolation. A simplified polynomial selection scheme is proposed to pass only one pair of locator and evaluator to successive decoding steps and a low-complexity parallel Chien search architecture is developed to implement this selection scheme. With the proposed polynomial selection architecture, the interpolation can run at the full speed to greatly increase the throughput. After efficient architectures and effective optimizations are employed, a generalized hardware complexity analysis is provided for the proposed interpolationbased decoder. For a (255, 239) RS code, the highspeed interpolation-based one-pass GMD decoder can achieve 53% higher throughput than the Kötter's decoder with slightly more hardware requirement. In terms of speed-over-area ratio, our design is 51% more efficient. In addition, compared to other soft-decision decoders, the high-speed interpolation-based GMD decoder can achieve better performance-complexity tradeoff.

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A rate-distortion perspective on multiple decoding attempts for Reed-Solomon codes

Nguyen

Pfister

Narayanan

2009

2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Recently, a number of authors have proposed decoding schemes for Reed-Solomon (RS) codes based on multiple trials of a simple RS decoding algorithm. In this paper, we present a rate-distortion (R-D) approach to analyze these multiple-decoding algorithms for RS codes. This approach is first used to understand the asymptotic performance-versuscomplexity trade-off of multiple error-and-erasure decoding of RS codes. By defining an appropriate distortion measure between an error pattern and an erasure pattern, the condition for a single error-and-erasure decoding to succeed reduces to a form where the distortion is compared to a fixed threshold. Finding the best set of erasure patterns for multiple decoding trials then turns out to be a covering problem which can be solved asymptotically by rate-distortion theory. Next, this approach is extended to analyze multiple algebraic soft-decision (ASD) decoding of RS codes. Both analytical and numerical computations of the R-D functions for the corresponding distortion measures are discussed. Simulation results show that proposed algorithms using this approach perform better than other algorithms with the same complexity.

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Reliability-Based Forward Recursive Algorithms for Algebraic Soft-Decision Decoding of Reed--Solomon Codes

Cited by 9 publications

References 23 publications

A Chase-GMD Algorithm for Soft-Decision Decoding of Reed-Solomon Codes on Perpendicular Recording Channels

A Chase-GMD Algorithm for Soft-Decision Decoding of Reed-Solomon Codes on Perpendicular Recording Channels

Efficient Generalized Minimum-distance Decoders of Reed-Solomon Codes

A rate-distortion perspective on multiple decoding attempts for Reed-Solomon codes

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