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IEEE TRANSACTIONS ON INFORMATION THEORY 2014年第4期60卷 2038-2053页

作者： Lee, Kwankyu Bras-Amoros, Maria O'Sullivan, Michael E. Chosun Univ Dept Math & Educ Kwangju 501759 South Korea Univ Rovira & Virgili Dept Comp Engn & Math E-43007 Tarragona Spain San Diego State Univ Dept Math & Stat San Diego CA 92182 USA

A unique decoding algorithm for general AG codes, namely multipoint evaluation codes on algebraic curves, is presented. It is a natural generalization of the previous decoding algorithm which was only for one-point AG codes. As such, it retains the same advantages of fast speed, regular structure, and direct message recovery. Upon this generalization, we add a technique from the Guruswami-Sudan list decoding that boosts the decoding speed significantly. Compared with other known decoding algorithms for general AG codes, it has a similar decoding performance and allows streamlined practical implementation by its simple and regular structure.

关键词： Multipoint AG code decoding algorithm interpolation Grobner base

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A projection decoding of a binary extremal self-dual code of length 40

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DESIGNS CODES AND CRYPTOGRAPHY 2017年第3期83卷 589-609页

作者： Kim, Jon-Lark Lee, Nari Sogang Univ Dept Math Seoul 121742 South Korea

As far as we know, there is no decoding algorithm of any binary self-dual [40, 20, 8] code except for the syndrome decoding applied to the code directly. This syndrome decoding for a binary self-dual [40, 20, 8] code is not efficient in the sense that it cannot be done by hand due to a large syndrome table. The purpose of this paper is to give two new efficient decoding algorithms for an extremal binary doubly-even self-dual [40, 20, 8] code by hand with the help of a Hermitian self-dual [10, 5, 4] code over GF(4). The main idea of this decoding is to project codewords of onto so that it reduces the complexity of the decoding of . The first algorithm is called the representation decoding algorithm. It is based on the pattern of codewords of . Using certain automorphisms of , we show that only eight types of codewords of can produce all the codewords of . The second algorithm is called the syndrome decoding algorithm based on . It first solves the syndrome equation in and finds a corresponding binary codeword of C-40, 1(D E).

关键词： decoding algorithm Projection Self-dual codes Syndrome decoding method

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Construction and decoding of matrix-product codes from nested codes

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APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING 2009年第5-6期20卷 497-507页

作者： Hernando, Fernando Lally, Kristine Ruano, Diego Natl Univ Ireland Univ Coll Cork Dept Math Cork Ireland RMIT Univ Dept Math & Stat Melbourne Vic Australia Tech Univ Denmark Dept Math DK-2800 Lyngby Denmark

We consider matrix-product codes [C(1)...C(S)] . A, where C(1),...,C(S) are nested linear codes and matrix A has full rank. We compute their minimum distance and provide a decoding algorithm when A is a non-singular b... 详细信息

关键词： Linear codes Matrix-product codes decoding algorithm Minimum distance Quasi-cyclic codes

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New Constructions of q-Ary MDS Array Codes With Multiple Parities and Their Effective decoding

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IEEE TRANSACTIONS ON INFORMATION THEORY 2023年第11期69卷 7082-7098页

作者： Lv, Jingjie Fang, Weijun Chen, Xiangyu Yang, Jing Xia, Shu-Tao Tsinghua Univ Tsinghua Shenzhen Int Grad Sch Shenzhen 518055 Peoples R China Shandong Univ Key Lab Cryptol Technol & Informat Secur Minist Educ Qingdao 266237 Peoples R China Shandong Univ Sch Cyber Sci & Technol Qingdao 266237 Peoples R China Huawei Technol Co Ltd Shenzhen 518055 Guangdong Peoples R China

From the perspective of parity-check matrices, we present new constructions of q -ary maximum distance separable (MDS) array codes with multiple parities. Applying these constructions, some new types of MDS array codes with array numbers m-tau can be derived, where gcd(m,q)=1 . Moreover, an explicit construction of binary MDS array codes is also presented. Compared to the existing MDS array codes, one important characteristic of these codes is that their available code lengths are much longer, which is suitable for large-scale storage systems. In some particular cases, the maximum code lengths of these codes and their extension can be up to 2(m-tau) and 2(m-tau)+1 (or 2(m-tau)+2 ), respectively. Moreover, to demonstrate the applicability of our constructed MDS array codes, we present an effective generic decoding method for the erased errors. In particular, when there are no more than three erasures occurring, a scheduled algorithm for the syndrome computation of our explicit construction is further proposed, whose computational complexity is asymptotically optimal. Furthermore, this algorithm can be directly applied to the encoding procedure of their extended form. The simulation shows that our new MDS array codes have better encoding and decoding performances than the corresponding extended RS codes coupled with different algorithms.

关键词： Codes decoding Redundancy Encoding Arrays Computational complexity Symbols Array codes maximum-distance separable codes quasi-cyclic codes Blaum-Roth codes Reed-Solomon codes decoding algorithm syndrome computation

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LDPC decoding with locally informed dynamic scheduling based on the law of large numbers

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IET COMMUNICATIONS 2022年第6期16卷 634-648页

作者： Liang, Shuo Xie, Suipeng Liu, Xingcheng Wang, Zhongfeng Sun Yat Sen Univ Sch Elect & Informat Technol SEIT Guangzhou Peoples R China Guangzhou Xinhuo Univ Sch Informat Sci Guangzhou Peoples R China Southern Marine Sci & Engn Guangdong Lab Zhuhai Innovat Team Estuary Coast & Isl Reef Engn Zhuhai Peoples R China Nanjing Univ Sch Elect Sci & Engn Nanjing Peoples R China

The informed dynamic scheduling (IDS) strategies, in which the edge message with the maximum message-residual is updated preferentially, achieve remarkable error-correction performance when applied to low-density parity-check (LDPC) codes. However, the IDS strategies incur inferior convergence in iterative decoding owing to the greedy problem, which is called the update-relayed trend here. In order to solve the greediness, two locally informed dynamic scheduling algorithms based on the law of large numbers are proposed. The proposed decoding algorithms use random select of check nodes over a predefined update range (RSPUR) which effectively suppresses the propagation of the update-relayed trend and accordingly restrains the forming of multi-update cycles. Moreover, the decoding algorithm is further improved based on random select of check nodes over an adjustable update range (RSCAR). The update ranges are selected based on the law of large numbers. Therefore, the computational resources can be allocated more equitably by increasing iterations. Simulation results show that both the proposed algorithms achieve excellent performance in terms of throughput and convergence with low decoding complexity over the Additive White Gaussian Noise (AWGN) and the fading channels compared to the previous IDS strategies. Hence, the proposed algorithms behave excellently over the wireless channels.

关键词： maximum message residual error correction performance multiupdate cycles fading channels LDPC inferior convergence wireless channels check nodes AWGN channels low density parity check codes edge message telecommunication scheduling low decoding complexity IDS strategies informed dynamic scheduling strategies adjustable update range parity check codes predefined update range iterative decoding channel coding greedy problem locally informed dynamic scheduling algorithms iterative decoding owing decoding algorithm

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Algebraic decoding of a Class of Binary Cyclic Codes Via Lagrange Interpolation Formula

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IEEE TRANSACTIONS ON INFORMATION THEORY 2010年第1期56卷 130-139页

作者： Chang, Yaotsu Lee, Chong-Dao I Shou Univ Dept Appl Math Kaohsiung 84001 Taiwan I Shou Univ Dept Commun Engn Kaohsiung 84001 Taiwan

In this paper, three algebraic decoding algorithms are proposed for the binary quadratic residue (QR) codes generated by irreducible polynomials. The polynomial relations among the syndromes and the coefficients of the error-locator polynomials have been computed with Lagrange interpolation formula (LIF). Unlike some previous QR decoders, which may take several iterations to decode a corrupted word, the iteration number of the first two algorithms is at most one. The processes in the first algorithm are the calculation of consecutive syndromes, inverse-free Berlekamp-Massey algorithm (IFBMA), and the Chien search. One of Orsini-Sala's results on the structure of general error-locator polynomials is generalized and applied to derive the second (respectively, third) algorithm that consists of the determination of general error-locator polynomial (respectively, classical error-locator polynomials) and the Chien search. Finally, the (17, 9, 5), (23, 12, 7), and (41, 21, 9) QR decoders are illustrated and their complexity analyses are given.

关键词： decoding algorithm general error-locator polynomial Lagrange interpolation formula (LIF) quadratic residue (QR) code syndrome

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ON decoding UNEQUAL ERROR PROTECTION PRODUCT CODES

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IEEE TRANSACTIONS ON INFORMATION THEORY 1990年第4期36卷 890-895页

作者： STEVENS, P VRIJE UNIV BRUSSELS FAC APPL SCIB-1050 BRUSSELSBELGIUM

The decoding of unequal error protection product codes, which are a combination of linear unequal error protection (UEP) codes and product codes, is addressed. A nonconstructive proof of the existence of a good error-erasure-decoding algorithm is presented; however, obtaining the decoding procedure is still an open research problem. A particular subclass of UEP product codes is considered, including a decoding algorithm that is an extension of the Blokh-Zyablov decoding algorithm for product codes. For this particular subclass the decoding problem is solved.

关键词： decoding error protection inequalities Product codes Research Problems decoding algorithm

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New decoding algorithms for Matrix C in the 802.16e WiMAX Standard

New Decoding Algorithms for Matrix C in the 802.16e WiMAX St...

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IEEE Vehicular Technology Conference

作者： Young Gil Kim Norman C. Beaulieu Department of Electrical and Computer Engineering University of Seoul iCORE Wireless Communications Laboratory University of Alberta

ISBN: (纸本)9781467318808

We examine the decoding of Matrix C in the 802.16e WiMAX standard. An exhaustive search and zero-forcing (ES-ZF) decoder and an exhaustive search and nulling canceling (ES-NC) decoder are proposed for uncoded systems. The computational complexity of Matrix C decoding using the ES-ZF decoder is shown to be the same as the complexity of the ZF decoder for Matrix B decoding with twice the number of receive antennas times the complexity of the maximum likelihood (ML) decoder for Matrix B decoding with twice the number of receive antennas. Matrix C can be implemented in a 2×2 multiple-input multiple-output (MEMO) system using the ES-NC decoder with reduced complexity compared to ML decoding with no performance loss. For coded systems, double pruned trees using a zero-forcing (DPT-ZF) algorithm or nulling canceling (DPT-NC) algorithm are proposed. The DPT-NC decoder can be implemented in a 2×2 MIMO coded system with reduced complexity compared to the Max-Log decoding with no performance loss.

关键词： Matrix C Space-time codes WiMAX standard decoding decoders decoding algorithm exhaustive search Coding systems matrices WiMax Complexity

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CONSTRUCTION AND decoding OF A CLASS OF ALGEBRAIC-GEOMETRY CODES

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IEEE TRANSACTIONS ON INFORMATION THEORY 1989年第4期35卷 811-821页

作者： JUSTESEN, J LARSEN, KJ JENSEN, HE HAVEMOSE, A HOHOLDT, T TECH UNIV DENMARK INST MATHDK-2800 LYNGBYDENMARK

A class of codes derived from algebraic plane curves is constructed. The concepts and results from algebraic geometry that were used are explained in detail; no further knowledge of algebraic geometry is needed. Parameters, generator and parity-check matrices are given. The main result is a decoding algorithm which turns out to be a generalization of the Peterson algorithm for decoding BCH decoder codes.

关键词： decoding Codes check matrix Algebraic Geometry decoding algorithm plane curve

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SEQUENTIAL-decoding FOR MULTIPLE ACCESS CHANNELS

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IEEE TRANSACTIONS ON INFORMATION THEORY 1988年第2期34卷 246-259页

作者： ARIKAN, E IEEE

The use of sequential decoding in multiple access channels is considered. The Fano metric, which achieves all achievable rates in the one-user case, fails to do so in the multiuser case. A new metric is introduced and an inner bound is given to its achievable rate region. This inner bound region is large enough to encourage the use of sequential decoding in practice. The new metric is optimal, in the sense of achieving all achievable rates, in the case=of one-user and painvise-reversible chan- nels. Whether the metic is optimal for all multiple access channels remains an open problem. It is worth noting that even in the one-user case, the new metric differs from the Fano metric in a nontrivial way, showing that the Fano metric is not uniquely optimal for such channels. A new and stricter criterion of achievability in sequential decoding is also introduced and examined.

关键词： .multiuser denote notation decoding algorithm inner bound achievability alphabets channel output Fano tree codes

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