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IEEE TRANSACTIONS ON INFORMATION THEORY 1995年第5期41卷 1290-1302页

作者： FITZPATRICK, P University Coll Cork Irel

We consider the set M = {(a, b): a = bh mod x(2t)} of all solutions of the key equation for alternant codes, where h is the syndrome polynomial. In decoding these codes a particular solution (omega, sigma) is an element of M is sought, subject to omega and sigma being relatively prime and satisfying certain degree conditions. We prove that these requirements specify (omega, sigma) uniquely as the minimal element of M (analogous to the monic polynomial of minimal degree generating an ideal of F[x]) with respect to a certain term order and that, as such, (w, a) may be determined from an appropriate Grobner basis of M. Motivated by this and other variations of the key equation (such as that appropriate to errors-and-erasures decoding) we derive a general algorithm for solving the congruence a = bg mod x(n) for a range of term orders defined by the conditions on the particular solution required. Our techniques provide a unified approach to the solution of these key equations.

关键词： GROBNER BASIS ALTERNANT CODE decoding algorithms ERRORS-AND-ERASURES

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Multiple-access hyperchannel

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PROBLEMS OF INFORMATION TRANSMISSION 2013年第4期49卷 299-307页

作者： Bassalygo, L. A. Rykov, V. V. Russian Acad Sci Kharkevich Inst Informat Transmiss Problems Moscow 117901 Russia Univ Nebraska Dept Math Omaha NE 68182 USA

We derive an asymptotic upper bound on the decoding failure probability for an MDS code in a q-ary multiple access channel.

关键词： MULTIPLE access protocols (Computer network protocols) RESEARCH decoding algorithms PROBABILITY theory BAYESIAN analysis GRAPH theory

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Universal topological phase of two-dimensional stabilizer codes

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NEW JOURNAL OF PHYSICS 2012年第7期14卷 1-21页

作者： Bombin, H. Duclos-Cianci, Guillaume Poulin, David Univ Sherbrooke Dept Phys Sherbrooke PQ J1K 2R1 Canada Perimeter Inst Theoret Phys Waterloo ON N2L 2Y5 Canada

Topological phases can be defined in terms of local equivalence: two systems are in the same topological phase if it is possible to transform one into the other by a local reorganization of its degrees of freedom. The classification of topological phases therefore amounts to the classification of long-range entanglement. Such local transformation could result, for instance, from the adiabatic continuation of one system's Hamiltonian to the other. Here, we use this definition to study the topological phase of translationally invariant stabilizer codes in two spatial dimensions, and show that they all belong to one universal phase. We do this by constructing an explicit mapping from any such code to a number of copies of Kitaev's code. Some of our results extend to some two-dimensional (2D) subsystem codes, including topological subsystem codes. Error correction benefits from the corresponding local mappings. In particular, it enables us to use decoding algorithm developed for Kitaev's code to decode any 2D stabilizer code and subsystem code.

关键词： EQUIVALENCE principle (Physics) DEGREES of freedom HAMILTONIAN systems decoding algorithms TWO-dimensional models

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Energy-Efficient Multi-Job Scheduling Model for Cloud Computing and Its Genetic Algorithm

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MATHEMATICAL PROBLEMS IN ENGINEERING 2012年第1期2012卷 1-16页

作者： Wang, Xiaoli Wang, Yuping Zhu, Hai Xidian Univ Sch Comp Sci & Technol Xian 710071 Shaanxi Peoples R China Zhoukou Normal Univ Sch Comp Sci & Technol Zhoukou 466001 Peoples R China

For the problem that the energy efficiency of the cloud computing data center is low, from the point of view of the energy efficiency of the servers, we propose a new energy-efficient multi-job scheduling model based on Google's massive data processing framework. To solve this model, we design a practical encoding and decoding method for the individuals and construct an overall energy efficiency function of the servers as the fitness value of each individual. Meanwhile, in order to accelerate the convergent speed of our algorithm and enhance its searching ability, a local search operator is introduced. Finally, the experiments show that the proposed algorithm is effective and efficient.

关键词： CLOUD computing DATA libraries ELECTRONIC data processing algorithms decoding algorithms

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A quantitative model for the rate-limiting process of UGA alternative assignments to stop and selenocysteine codons

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PLOS COMPUTATIONAL BIOLOGY 2017年第2期13卷 e1005367-e1005367页

作者： Chen, Yen-Fu Lin, Hsiu-Chuan Chuang, Kai-Neng Lin, Chih-Hsu Yen, Hsueh-Chi S. Yeang, Chen-Hsiang Acad Sinica Inst Mol Biol Taipei Taiwan Natl Taiwan Univ Genome & Syst Biol Degree Program Taipei Taiwan Acad Sinica Taipei Taiwan Acad Sinica Inst Stat Sci Taipei Taiwan

Ambiguity in genetic codes exists in cases where certain stop codons are alternatively used to encode non-canonical amino acids. In selenoprotein transcripts, the UGA codon may either represent a translation termination signal or a selenocysteine (Sec) codon. Translating UGA to Sec requires selenium and specialized Sec incorporation machinery such as the interaction between the SECIS element and SBP2 protein, but how these factors quantitatively affect alternative assignments of UGA has not been fully investigated. We developed a model simulating the UGA decoding process. Our model is based on the following assumptions: (1) charged Sec-specific tRNAs (Sec-tRNA Sec) and release factors compete for a UGA site, (2) Sec-tRNA Sec abundance is limited by the concentrations of selenium and Sec-specific tRNA (tRNA Sec) precursors, and (3) all synthesis reactions follow first-order kinetics. We demonstrated that this model captured two prominent characteristics observed from experimental data. First, UGA to Sec decoding increases with elevated selenium availability, but saturates under high selenium supply. Second, the efficiency of Sec incorporation is reduced with increasing selenoprotein synthesis. We measured the expressions of four selenoprotein constructs and estimated their model parameters. Their inferred Sec incorporation efficiencies did not correlate well with their SECIS-SBP2 binding affinities, suggesting the existence of additional factors determining the hierarchy of selenoprotein synthesis under selenium deficiency. This model provides a framework to systematically study the interplay of factors affecting the dual definitions of a genetic codon.

关键词： SELENOCYSTEINE QUANTITATIVE research GENETIC code decoding algorithms BIOSYNTHESIS

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Correcting Spanning Errors With a Fractal Code

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IEEE TRANSACTIONS ON INFORMATION THEORY 2021年第7期67卷 4504-4516页

作者： Nixon, Georgia M. Brown, Benjamin J. Univ Sydney Sch Phys Ctr Engn Quantum Syst Sydney NSW 2006 Australia Univ Cambridge Cavendish Lab Cambridge CB3 0HE England Univ Sydney Sch Phys Ctr Engn Quantum Syst Sydney NSW 2006 Australia

The strongly correlated systems we use to realise quantum error-correcting codes may give rise to high-weight, problematic errors. Encouragingly, we can expect local quantum error-correcting codes with no string-like logical operators - such as the cubic code - to be robust to highly correlated, one-dimensional errors that span their lattice. The challenge remains to design decoding algorithms that utilise the high distance of these codes. Here, we begin the development of such algorithms by proposing an efficient decoder for the 'Fibonacci code';a two-dimensional classical code that mimics the fractal nature of the cubic code. Our iterative decoder finds a correction through repeated use of minimum-weight perfect matching by exploiting symmetries of the code. We perform numerical experiments that show our decoder is robust to one-dimensional, correlated errors. First, using a bit-flip noise model at low error rates, we find that our decoder demonstrates a logical failure rate that scales super exponentially in the linear size of the lattice. In contrast, a decoder that could not tolerate spanning errors would not achieve this rapid decay in failure rate with increasing system size. We also find a finite threshold using a spanning noise model that introduces string-like errors that stretch along full rows and columns of the lattice. These results provide direct evidence that our decoder is robust to one-dimensional, correlated errors that span the lattice.

关键词： decoding Lattices Fractals Faces Qubit Runtime Error correction codes Classical coding theory fractal codes decoding algorithms minimum-weight perfect matching quantum error correction fracton topological codes

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Directions in polynomial reconstruction based cryptography

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2004年第5期E87A卷 978-985页

作者： Kiayias, A Yung, M Univ Connecticut Dept Comp Sci & Engn Storrs CT 06269 USA Columbia Univ Dept Comp Sci New York NY 10027 USA

Cryptography and Coding Theory are closely related in many respects. Recently, the problem of "decoding Reed Solomon codes" (also known as "polynomial reconstruction") was suggested as an intractability assumption to base the security of protocols on. This has initiated a line of cryptographic research exploiting the rich algebraic structure of the problem and its variants. In this paper we give a short overview of the recent works in this area as well as list directions and open problems in Polynomial Reconstruction Based Cryptography.

关键词： cryptography coding theory decoding algorithms Reed Solomon codes polynomial reconstruction intractability assumptions

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Near-Optimal Sparsity-Constrained Group Testing: Improved Bounds and algorithms

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IEEE TRANSACTIONS ON INFORMATION THEORY 2022年第5期68卷 3253-3280页

作者： Gebhard, Oliver Hahn-Klimroth, Max Parczyk, Olaf Penschuck, Manuel Rolvien, Maurice Scarlett, Jonathan Tan, Nelvin Tech Univ Dortmund Fac Comp Sci D-44227 Dortmund Germany FU Berlin Dept Math & Comp Sci D-14195 Berlin Germany Goethe Univ Frankfurt Inst Comp Sci D-60325 Frankfurt Germany Natl Univ Singapore Dept Comp Sci Singapore 117418 Singapore Univ Cambridge Dept Engn Cambridge CB2 1PZ England

Recent advances in noiseless non-adaptive group testing have led to a precise asymptotic characterization of the number of tests required for high-probability recovery in the sublinear regime k = n(theta) (with theta is an element of(0, 1)), with n individuals among which k are infected. However, the required number of tests may increase substantially under real-world practical constraints, notably including bounds on the maximum number Delta of tests an individual can be placed in, or the maximum number Gamma of individuals in a given test. While previous works have given recovery guarantees for these settings, significant gaps remain between the achievability and converse bounds. In this paper, we substantially or completely close several of the most prominent gaps. In the case of Delta-divisible items, we show that the definite defectives (DD) algorithm coupled with a random regular design is asymptotically optimal in dense scaling regimes, and optimal to within a factor of e more generally;we establish this by strengthening both the best known achievability and converse bounds. In the case of Gamma-sized tests, we provide a comprehensive analysis of the regime Gamma = Theta(1), and again establish a precise threshold proving the asymptotic optimality of SCOMP (a slight refinement of DD) equipped with a tailored pooling scheme. Finally, for each of these two settings, we provide near-optimal adaptive algorithms based on sequential splitting, and provably demonstrate gaps between the performance of optimal adaptive and non-adaptive algorithms.

关键词： Group testing sparsity information-theoretic limits decoding algorithms bayesian inference fragile complexity

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A survival duration-guided NSGA-III for sustainable flexible job shop scheduling problem considering dual resources

IET COLLABORATIVE INTELLIGENT MANUFACTURING

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IET COLLABORATIVE INTELLIGENT MANUFACTURING 2021年第2期3卷 119-130页

作者： Li Hongyu Wu Xiuli Univ Sci & Technol Beijing Sch Mech Engn Dept Logist Engn Beijing Peoples R China

Considering the increasing concern on sustainable development from manufacturers, focus is given to three kinds of indicators of sustainable development, that is, economy, environment, and society, and schedule two types of resource, that is machines and workers, simultaneously in the classical flexible job shop scheduling problem. The authors define it as a sustainable flexible job shop scheduling problem considering dual resources (SFJSPCDR). First, a model of the SFJSPCDR is formulated to optimise the makespan, the energy consumption, and the ergonomic risk simultaneously. Second, an improved survival duration-guided NSGA-III algorithm (SDG-NSGA-III) is proposed to solve SFJSPCDR. The survival duration of each individual determines whether it takes part in generating offspring. In order to balance the energy consumption and ergonomic risk while minimising the makespan, a double-low decoding algorithm is proposed, which is composed of two decoding algorithms. Cross-generation selection is employed with the non-dominated sorting, and the next-generation population is selected according to the reference point-based selection strategy. In addition, a restart strategy is also integrated to improve the exploration and exploitation performance of the SDG-NSGA-III algorithm. Finally, a group of experiments are carried out and the results prove the effectiveness of the proposed algorithm.

关键词： decoding algorithms sustainable flexible job shop scheduling dual resources ergonomic risk sustainable development job shop scheduling ergonomics energy consumption survival duration-guided NSGA-III algorithm cross-generation selection minimisation SDG-NSGA-III algorithm nondominated sorting SFJSPCDR next-generation population genetic algorithms

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Single trial analysis of field potentials in perception, learning and memory

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CURRENT OPINION IN NEUROBIOLOGY 2015年 31卷 148-155页

作者： Rey, Hernan Gonzalo Ahmadi, Maryam Quiroga, Rodrigo Quian Univ Leicester Ctr Syst Neurosci Leicester LE1 7QR Leics England

The analysis of single trial responses of field potentials is an important tool to study brain signals. Single trial analyses can indeed provide additional information that is obscured or simply not available in the average responses The importance of studying single trial responses is reinforced by the fact that different brain processes are correlated with trial-by-trial variation of the responses. Here, we review key studies implementing single trial analyses of field potentials using methods such as single trial latency, amplitude and power changes, spike and LFP relationships, correlations between areas, cross frequency coupling, decoding of the presented stimuli that bring light into the neural basis of perception, learning and memory.

关键词： PERCEPTION COGNITIVE ability decoding algorithms HISTOGRAMS RAYLEIGH model PSYCHOLOGICAL aspects

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