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Theory and Applications of Network Error Correction Coding

PROCEEDINGS OF THE IEEE 2011年第3期99卷 406-420页

作者： Zhang, Zhen Univ So Calif Inst Commun Sci Dept Elect Engn Syst Los Angeles CA 90089 USA

Network error correction coding (NEC) has attracted a lot of attention in recent years because of its potential usefulness in network communications. Several kinds of errors may occur in communication networks using network coding. This includes random errors, erasures, and errors caused by attacks from malicious nodes. The main goal of the theory of NEC is to deal with these errors efficiently. Two kinds of network models have been considered in network coding theory: coherent and noncoherent networks. A network is called coherent if network characteristics are known to senders and receivers, and called noncoherent if they are unknown. Although both scenarios are theoretically interesting, the noncoherent network model fits better to the requirements in most applications. So far, there are two lines of research in the theory of NEC. One approach follows the classical method by representing messages by sequences and the other approach uses the theory of rank metric codes for network error correction by representing messages by subspaces. Following both approaches, basic theories have been developed. This includes the formulation of channel models, the characterization of error correction/detection capabilities for various kinds of errors, the derivation of bounds for NECs, the study of existence and constructions of optimal codes, the development of encoding and decoding techniques, and the design of code suitable for real applications. In this paper, we summarize some important contributions in this research direction.

关键词： Attacks from malicious nodes decoding algorithms erasures maximum distance separable code network coding network error correction coding (NEC) product code rank metric code singleton bound subspace code

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Low-density parity-check codes based on steiner systems and permutation matrices

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PROBLEMS OF INFORMATION TRANSMISSION 2013年第4期49卷 333-347页

作者： Ivanov, F. I. Zyablov, V. V. Russian Acad Sci Kharkevich Inst Informat Transmiss Problems Moscow 117901 Russia

An algorithm for generating parity-check matrices of regular low-density paritycheck codes based on permutation matrices and Steiner triple systems S(v, 3, 2), v = 2 (m) - 1, is proposed. Estimations of the rate, minimum distance, and girth for obtained code constructions are presented. Results of simulation of the obtained code constructions for an iterative "belief propagation" (Sum-Product) decoding algorithm applied in the case of transmission over a binary channel with additive Gaussian white noise and BPSK modulation are presented.

关键词： PARITY-check matrix LOW density parity check codes PERMUTATION indexes STEINER systems decoding algorithms GAUSSIAN distribution

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Rare Earth Core/Shell Nanobarcodes for Multiplexed Trace Biodetection

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ANALYTICAL CHEMISTRY 2015年第11期87卷 5745-5752页

作者： Chen, Lei Li, Xiaomin Shen, Dengke Zhou, Lei Zhu, Dan Fan, Chunhai Zhang, Fan Fudan Univ Dept Chem IChEm Collaborat Innovat Ctr Chem Energy Mat State Key Lab Mol Engn Polymers Shanghai 200433 Peoples R China Chinese Acad Sci Shanghai Inst Appl Phys Phys Biol Lab Shanghai 201800 Peoples R China Chinese Acad Sci Ctr Environm & Energy Nanomat Anhui Key Lab Nanomat & Nanotechnol Key Lab Mat PhysInst Solid State PhysHefei Inst Hefei 230031 Peoples R China

Multiplexed detection technology has been attractive for its simultaneous assay of several analytes, which play significant roles in applications such as Screening for combinatorial chemistry, genetic analysis, and clinical diagnostics. This work reports a novel and potentially powerful encoding system based upon dispersible suspension arrays of multilayer rare earth core/shell nanoparticles that are capable of multiplexed, high-sensitivity reporting for biomolecule detection by the Z-contrast imaging. These nanobarcode arrays are encoded by nanostructure design based on different atomic numbers. With the Well-resolved high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) decoding technique, many thousands of unique nanobarcodes can be identified by multilayer core/shell nanostructure. Their applications to multiplexed biodetection of DNA demonstrated the highly sensitive (picomole) features of this novel nanobarcode system.

关键词： BAR codes RARE earth metal compounds COMBINATORIAL chemistry NANOPARTICLES BIOMOLECULES SCANNING transmission electron microscopy decoding algorithms DNA

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Noncoherent Spectral Optical CDMA System Using 1D Active Weight Two-Code Keying Codes

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MATHEMATICAL PROBLEMS IN ENGINEERING 2016年第1期2016卷 1-9页

作者： Yeh, Bih-Chyun Chang Gung Univ Coll Engn Sch Elect & Comp Engn Dept Elect Engn Taoyuan Taiwan

We propose a new family of one-dimensional (1D) active weight two-code keying (TCK) in spectral amplitude coding (SAC) optical code divisionmultiple access (OCDMA) networks. We use encoding and decoding transfer functions to operate the 1D active weight TCK. The proposed structure includes an optical line terminal (OLT) and optical network units (ONUs) to produce the encoding and decoding codes of the proposed OLT and ONUs, respectively. The proposed ONU uses the modified cross-correlation to remove interferences from other simultaneous users, that is, the multiuser interference (MUI). When the phase-induced intensity noise (PIIN) is the most important noise, the modified cross-correlation suppresses the PIIN. In the numerical results, we find that the bit error rate (BER) for the proposed system using the 1D active weight TCK codes outperforms that for two other systems using the 1D M-Seq codes and 1D balanced incomplete block design (BIBD) codes. The effective source power for the proposed system can achieve -10 dBm, which has less power than that for the other systems.

关键词： CODE division multiple access TRANSFER functions (Mathematics) decoding algorithms INTERFERENCE (Telecommunication) BLOCK designs NUMERICAL analysis

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Bayesian analysis of interference cancellation for Alamouti multiplexing

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IEEE TRANSACTIONS ON INFORMATION THEORY 2008年第10期54卷 4755-4761页

作者： Sirianunpiboon, Songsri Calderbank, A. Robert Howard, Stephen D. Def Sci & Technol Org Edinburgh 5111 Australia Princeton Univ Princeton NJ 08544 USA

Space-time codes built out of Alamouti components have been adopted in wireless standards such as UNITS, IEEE 802.11n, and IEEE 802.16, where they facilitate higher data rates through multiplexing of parallel data streams and the addition of two or more antennas at the receiver that perform interference cancellation. This correspondence provides new theoretical insight into different algorithms for interference cancellation through a Bayesian analysis that expresses performance as a function of signal-to-noise ratio (SNR) in terms of the "angles" between different space-time coded data streams.

关键词： Alamouti code Bayesian analysis decoding algorithms interference cancellation quaternion arithmetic space-time block codes

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UnsupervisedWord Segmentation with Bi-directional Neural Language Model

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ACM TRANSACTIONS ON ASIAN AND LOW-RESOURCE LANGUAGE INFORMATION PROCESSING 2023年第1期22卷 1-16页

作者： Wang, Lihao Zheng, Xiaoqing Fudan Univ 220 Handan Rd Shanghai Peoples R China

We propose an unsupervised word segmentation model, in which for each unlabelled sentence sample, the learning objective is to maximize the generation probability of the sentence given its all possible segmentations. Such a generation probability can be factorized into the likelihood of each possible segment given the context in a recursive way. To capture both the long- and short-term dependencies, we propose to use a bi-directional neural language model to better extract the features of the segment's context. Two decoding algorithms were also developed to combine the context features from both directions to generate the final segmentation at the inference time, which helps to reconcile word-boundary ambiguities. Experimental results show that our context-sensitive unsupervised segmentation model achieved state-of-the-art at different evaluation settings on various datasets for Chinese, and the comparable result for Thai.

关键词： Unsupervised word segmentation bi-directional neural language model recurrent neural networks context-sensitive segmentation decoding algorithms

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The burst error correcting capabilities of a simple array code

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IEEE TRANSACTIONS ON INFORMATION THEORY 2005年第2期51卷 722-728页

作者： Raphaeli, D Tel Aviv Univ Fac Engn Dept Elect Engn Syst IL-69978 Tel Aviv Israel

We propose a simple decoder for a widely used array code, known as the EVENODD code, which is originally designed to correct phased burst errors, to make it useful for correcting nonphased errors. The proposed scheme is capable of correcting almost all bursts up to a certain length. We show that the failure rate is sufficiently small and approaches zero as the block length increases. The redundancy of the code is twice the maximal burst length, which is a lower bound for the redundancy of a true burst-error-correcting code. Both the encoder and the decoder have very low complexity, both in terms of number of operations and in terms of computer code size.

关键词： burst-error-correcting codes decoding algorithms error-correcting codes

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Power error locating pairs

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DESIGNS CODES AND CRYPTOGRAPHY 2020年第8期88卷 1561-1593页

作者： Couvreur, Alain Panaccione, Isabella INRIA 1 Rue Honore Estienne OrvesCampus Ecole Polytech F-91120 Palaiseau France Ecole Polytech UMR 7161 CNRS LIX F-91128 Palaiseau France

We present a new decoding algorithm based on error locating pairs and correcting an amount of errors exceeding half the minimum distance. When applied to Reed-Solomon or algebraic geometry codes, the algorithm is a reformulation of the so-calledpower decodingalgorithm. Asymptotically, it corrects errors up to Sudan's radius. In addition, this new framework applies to any code benefiting from an error locating pair. Similarly to Pellikaan's and Kotter's approach for unique algebraic decoding, our algorithm provides a unified point of view for decoding codes with an algebraic structure beyond the half minimum distance. It permits to get an abstract description of decoding using only codes and linear algebra and without involving the arithmetic of polynomial and rational function algebras used for the definition of the codes themselves. Such algorithms can be valuable for instance for cryptanalysis to construct a decoding algorithm of a code without having access to the hidden algebraic structure of the code.

关键词： Error correcting codes Reed-Solomon codes Algebraic geometry codes decoding algorithms Power decoding Error correcting pairs Cyclic codes

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Hidden Markov model framework for industrial maintenance activities

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART O-JOURNAL OF RISK AND RELIABILITY 2014年第3期228卷 230-242页

作者： Robles, Bernard Avila, Manuel Duculty, Florent Vrignat, Pascal Begot, Stephane Kratz, Frederic Univ Orleans UT Indre PRISME Lab EA 4229 Chateauroux France Univ Orleans ENSI PRISME Lab EA 4229 Bourges France

This article deals with modelization of industrial process by using hidden Markov model. The process is seen as a discrete event system. We propose different structures based on Markov automata, called topologies. A synthetic hidden Markov model is designed in order to match to a real industrial process. The models are intended to decode industrial maintenance observations (also called "symbol"). Symbols are produced with a corresponding degradation level (also called "state"). These 2-tuple (symbol, state) are known as Markov chains, also called "a signature." Hence, these various 2-tuple are implemented in the proposed topologies by using the Baum-Welch learning algorithm (decoding by forward variable) and the segmental K-means learning (decoding by Viterbi). We assess different frameworks (topology, learning and decoding algorithm, distribution) by relevancy measurements on model outputs. Then, we determine the most relevant framework for use in maintenance activities. Afterward, we try to minimize the size of the learning data. Thus, we could evaluate the model by using "sliding windows" of data. Finally, an industrial application is developed and compared with this framework. Our goal is to improve worker safety, maintenance policy, process reliability and reduce CO2 emissions in the industrial sector.

关键词： Hidden Markov model model selection predictive maintenance learning algorithms decoding algorithms statistical tests uncertainties

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Codes for MIMO transmission based on orthogonal sequences

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PROBLEMS OF INFORMATION TRANSMISSION 2011年第4期47卷 305-326页

作者： Kreshchuk, A. A. Davydov, A. A. Zyablov, V. V. Russian Acad Sci Kharkevich Inst Informat Transmiss Problems Moscow 117901 Russia

We consider MIMO communication systems with Rayleigh fading. We propose a new coded modulation based on orthogonal sequences and state a new decodability condition. We introduce concepts and constructions of permutation free (PF) and permutation and repetition free (PRF) codes. We also propose a construction of PRF codes with sign manipulation, whose code rate can exceed 1. For better analysis and construction of these codes we introduce a one-to-one mapping that transforms signal matrices to vectors over a finite field. We propose construction algorithms for PF and PRF codes. We build PF and PRF codes with large cardinality, which in several case achieve the maximum cardinality. Simulation of the constructed codes and estimation of their performance was done in Simulink environment. Results show high error-correcting capability, which often reaches that of STBC codes with full transmit diversity.

关键词： MIMO systems MATHEMATICAL models ORTHOGONALIZATION (Numerical analysis) RAYLEIGH model decoding algorithms TRANSMITTING antennas

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