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A fast erasure deletion generalized minimum distance decoding for one-point algebraic-geometry codes

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2001年第10期E84A卷 2376-2382页

作者： Fujisawa, M Sakata, S Univ Electrocommun Grad Course Comp Sci & Informat Math Chofu Tokyo 1828585 Japan Univ Electrocommun Dept Informat & Commun Engn Chofu Tokyo 1828585 Japan

Before we gave a fast generalized minimum distance (GMD) decoding algorithm for one-point algebraic-geometry (AG) codes. In this paper, we propose another fast GMD decoding algorithm for these codes, where the present method includes an erasure deletion procedure while the past one uses an erasure addition procedure. Both methods find a minimal polynomial set of a given syndrome array, which is a candidate for an erasure-and-error locator polynomial set constrained with an erasure locator set of each size. Although both erasure addition and deletion GMD decoding algorithms have been established for one-dimensional algebraic codes such as RS codes, nothing but the erasure addition GMD decoding algorithm for multidimensional algebraic codes such as one-point AG codes have been given. The present erasure deletion GMD decoding algorithm is based on the Berlekamp-Massey-Sakata (BMS) algorithm from the standpoint of constrained multidimensional shift register synthesis. It is expected that both our past and present methods play a joint role in decoding for one-point AG codes up to the error correction bound.

关键词： one-point algebraic-geometry code generalized minimum distance decoding BMS algorithm erasure addition erasure deletion

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The Euclidean Algorithm for generalized minimum distance decoding of Reed-Solomon Codes

The Euclidean Algorithm for Generalized Minimum Distance Dec...

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IEEE Information Theory Workshop (ITW)

作者： Kampf, Sabine Bossert, Martin Univ Ulm Inst Telecommun & Appl Informat Theory D-89069 Ulm Germany

This paper presents a method to merge generalized minimum distance decoding of Reed-Solomon codes with the extended Euclidean algorithm. By merge, we mean that the steps performed in generalized minimum distance decod... 详细信息

ISBN: (纸本)9781424482641

关键词： Euclidean algorithm Reed-Solomon codes Reed-Solomon codes generalized minimum distance decoding

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ON THE PERFORMANCE AND COMPLEXITY OF A generalized minimum distance REED-SOLOMON decoding ALGORITHM

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INTERNATIONAL JOURNAL OF SATELLITE COMMUNICATIONS 1994年第4期12卷 333-359页

作者： PEILE, RE Racal Research Ltd Worton Grange Reading Berkshire RG2 OSB U.K.

The article reports on the characteristics of an algorithm that implements generalized minimum distance (GMD) decoding of Reed-Solomon codes. The algorithm uses the novel Welch-Berlekamp (WB) algorithm, as modified by Tze-Hua, in order to minimize the complexity of the decoder. Both the WB algorithm and the GMD extension of the WB algorithm are described in outline. The performance of the GMD algorithm was simulated on AWGN channels and fading channels. Results are presented both for RS and concatenated RS codes. The gains over conventional decoding are larger for fading channels than for AWGN conditions but seem useful in all cases. The complexities of the GMD algorithm and the WB algorithm are analysed and compared to that of conventional RS decoding algorithms.

关键词： ERROR CORRECTION REED-SOLOMON CODES CONCATENATED CODES REED-MULLER CODES decoding ALGORITHMS generalized minimum distance decoding WELCH-BERLEKAMP ALGORITHM BERLEKAMP-MASSEY ALGORITHM

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A sufficient condition for a generalized minimum distance Reed-Solomon decoder to ensure correct decoding

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 1997年第11期E80A卷 2066-2072页

作者： Kamiya, N CandC Research Laboratories NEC Corp. Kawasaki-shi 216 Japan

generalized minimum-distance (GMD) decoding is well-known as a soft decision decoding technique for such linear block codes as BCH and RS codes. The GMD decoding algorithm generates a set of candidate codewords and selects as a decoded codeword that candidate with the smallest reliable distance. In this paper, for a GMD decoder of RS and BCH codes, we present a new sufficient condition for the decoded codeword to be optimal, and we show that this sufficient condition is less stringent than the one presented by Taipale and Pursely.

关键词： Reed-Solomon codes BCH codes soft decision decoding generalized minimum distance decoding optimality

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Algebraic soft-decision decoding of Reed-Solomon codes using bit-level soft information

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IEEE TRANSACTIONS ON INFORMATION THEORY 2008年第9期54卷 3907-3928页

作者： Jiang, Jing Narayanan, Krishna R. Texas A&M Univ Dept Elect & Comp Engn College Stn TX 77843 USA

The performance of algebraic soft-decision decoding of Reed-Solomon codes using bit-level soft information is investigated. Optimal multiplicity assignment strategies for algebraic soft-decision decoding (SDD) with infinite cost are first studied over erasure channels and the binary-symmetric channel. The corresponding decoding radii are calculated in closed forms and tight bounds on the error probability are derived. The multiplicity assignment strategy and the corresponding performance analysis are then generalized to characterize the decoding region of algebraic SDD over a mixed error and bit-level erasure channel. The bit-level decoding region of the proposed multiplicity assignment strategy is shown to be significantly larger than that of conventional Berlekamp-Massey decoding. As an application, a bit-level generalized minimum distance decoding algorithm is proposed. The proposed decoding compares favorably with many other Reed-Solomon SDD algorithms over various channels. Moreover, owing to the simplicity of the proposed bit-level generalized minimum distance decoding, its performance can be tightly bounded using order statistics.

关键词： algebraic soft-decision decoding bit-level soft information error and erasure decoding generalized minimum distance decoding Guruswami-Sudan decoding Koetter-Vardy decoding list decoding multiplicity assignment Reed-Solomon codes

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Bounded distance plus 1 soft-decision Reed-Solomon decoding

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IEEE TRANSACTIONS ON INFORMATION THEORY 1996年第3期42卷 704-720页

作者： Berlekamp, E Hazelnut Berkeley CA USA

We present a new Reed-Solomon decoding algorithm, which embodies several refinements of an earlier algorithm. Some portions of this new decoding algorithm operate on symbols of length Igq bits;other portions operate on somewhat longer symbols. In the worst case, the total number of calculations required by the new decoding algorithm is proportional to nr, where n is the code's block length and r is its redundancy. This worst case workload is very similar to prior algorithms. But in many applications, average-case workload and error-correcting performance are both much better. The input to the new algorithm consists of n received symbols from GF(q), and rr nonnegative real numbers, each of which is the reliability of the corresponding received symbol. Any conceivable errata pattern has a ''score'' equal to the sum of the reliabilities of its locations with nonzero errata values. A max-likelihood decoder would find the minimum score over all possible errata patterns. Our new decoding algorithm finds the minimum score only over a subset of these possible errata patterns. The errata within any candidate errata pattern may be partitioned into ''errors'' and ''erasures,'' depending on whether the corresponding reliabilities are above or below an ''erasure threshold.'' Different candidate errata patterns may have different thresholds, each chosen to minimize its corresponding ERRATA COUNT, which is defined as 2 . (number of errors) c (number of erasures). The new algorithm finds an errata pattern with minimum score among all errata patterns for which ERRATA COUNT less than or equal to r + 1 where r is the redundancy of the RS code. This is one check symbol better than conventional RS decoding algorithms. Conventional algorithms also require that the erasure threshold be set a priori;the new algorithm obtains the best answer over all possible settings of the erasure threshold. Conventional cyclic RS codes have length n = q - 1, and their locations correspond to the nonzero

关键词： decoding algorithms Reed-Solomon codes soft decisions doubly extended codes algebraic decoding decoding beyond half minimum distance probabilistic decoding best case decoding queued decoding generalized minimum distance decoding bounded distance decoding

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AN EFFICIENT MAXIMUM-LIKELIHOOD-decoding ALGORITHM FOR LINEAR BLOCK-CODES WITH ALGEBRAIC DECODER

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IEEE TRANSACTIONS ON INFORMATION THEORY 1994年第2期40卷 320-327页

作者： KANEKO, T NISHIJIMA, T INAZUMI, H HIRASAWA, S WASEDA UNIV SCH SCI & ENGNDEPT IND ENGN & MANAGEMENTSHINJUKU KUTOKYO 169JAPAN KANAGAWA INST TECHNOL DEPT COMP SCI & ENGNATSUGI 24302JAPAN SHONAN INST TECHNOL DEPT INFORMAT SCIFUJISAWA 251JAPAN

A new soft decoding algorithm for linear codes is proposed. The decoding algorithm works with any algebraic decoder and its performance as strictly the same as that of maximum-likelihood-decoding (MLD . Since our decoding algorithm generates sets of different candidate codewords corresponding to the received sequence, is decoding complexity depends on the received sequence We compare our decoding algorithm with Chase algorithm 2 and the Tanaka-Kakigahara algorithm in which a similar method for generating candidate codewords is used. Computer simulation results indicate, for some signal-to-noise ratios (SNR), that our decoding algorithm requires less average complexity than those of the other two algorithms, but the performance of ours is always superior to those of the other two.

关键词： MAXIMUM-LIKELIHOOD decoding SOFT DECISION decoding generalized minimum distance decoding LINEAR BLOCK CODES

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On the implementation of soft-decision decoding for RS codes

On the implementation of soft-decision decoding for RS codes

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11th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC 2000)

作者： Mahmudi, A Benaissa, M Sweeney, P Sibley, MJN Univ Huddersfield Sch Engn Huddersfield HD1 3DH W Yorkshire England

This paper deals with the hardware implementation of soft decision decoding (SDD) of Reed-Solomon (RS) codes. An efficient algorithm for hardware implementation of generalized minimum distance (GMD) decoding of RS cod... 详细信息

ISBN: (纸本)0780364635

关键词： coding error correction Reed Solomon codes generalized minimum distance decoding Welch-Berlekamp algorithm soft decision decoding

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List decoding of concatenated codes: improved performance estimates

List decoding of concatenated codes: improved performance es...

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IEEE International Symposium on Information Theory

作者： Barg, A McGregor, A Univ Maryland College Pk MD 20742 USA

An improved bound is proved on the list-decoding radius of a concatenated code relying upon a combination of (soft-decision) algebraic list decoding and generalized minimum distance (GMD) decoding in the outer level. ... 详细信息

ISBN: (纸本)0780382803

关键词： random codes concatenated codes algebraic codes linear codes probability soft-decision algebraic list decoding generalized minimum distance decoding random linear code

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On Hard-Decision Forward Error Correction with Application to High-Throughput Fiber-Optic Communications

On Hard-Decision Forward Error Correction with Application t...

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作者： Alireza Sheikh Chalmers University of Technology

学位级别：博士

The advent of the Internet not only changed the communication methods signifi- cantly, but also the life-style of the human beings. The number of Internet users has grown exponentially in the last decade, and the number of users exceeded 3.4 billion in 2016. Fiber links serve as the Internet backbone, hence, the fast grow of the Internet network and the sheer of new applications is highly driven by advances in optical communications. The emergence of coherent optical systems has led to a more efficient use of the available spectrum compared to traditional on-oﬀ keying transmission, and has made it possible to increase the supported data rates. To achieve high spectral efficiencies and improve the transmission reach, coding in combination with a higher order modulation, a scheme known as coded modulation (CM), has become indispensable in fiber-optic communications. In the recent years, graph-based codes such as low-density parity-check codes and soft decision decoding (SDD) have been adopted for long-haul coherent optical systems. SDD yields very high net coding gains but at the expense of a relatively high decoding complexity, which brings implementation challenges at very high data rates. Hard decision de- coding (HDD) is an appealing alternative that reduces the decoding complexity. This motivates the focus of this thesis on forward error correction (FEC) with HDD for high-throughput, low power fiber-optic communications. In this thesis, we start by studying the performance bounds of HDD. In particular, we derive achievable information rates (AIRs) for CM with HDD for both bit-wise and symbol-wise decoding, and show that bit-wise HDD yields significantly higher AIRs. We also design nonbinary staircase codes using density evolution. Finite length simulation results of binary and nonbinary staircase codes corroborate the conclusions arising from the AIR analysis, i. e., for HDD binary codes are preferable. Then, we consider probabilistic shaping. In particular, we e

关键词： Achievable information rates bounded distance decoding coded modulation generalized minimum distance decoding hard decision decoding probabilistic shaping product codes product-like codes staircase codes

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