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List decoding of algebraic-geometric codes

IEEE TRANSACTIONS ON INFORMATION THEORY 1999年第2期45卷 432-437页

作者： Shokrollahi, MA Wasserman, H AT&T Bell Labs Murray Hill NJ 07974 USA Carnegie Mellon Univ Sch Comp Sci Pittsburgh PA 15213 USA

We generalize Sudan's results for Reed-Solomon codes to the class of algebraic-geometric codes, designing algorithms for list decoding of algebraic geometric codes which can decode beyond the conventional error-correction bound (d - 1)/2, d being the minimum distance of the code. Our main algorithm is based on an interpolation scheme and factorization of polynomials over algebraic function fields, For the latter problem we design a polynomial-time algorithm and show that the resulting overall list-decoding algorithm runs in polynomial time under some mild conditions. Several examples are included.

关键词： algebraic function fields algebraic-geometric codes decoding algorithms factorization of polynomials Reed-Solomon codes

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Review of brain encoding and decoding mechanisms for EEG-based brain-computer interface

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COGNITIVE NEURODYNAMICS 2021年第4期15卷 569-584页

作者： Xu, Lichao Xu, Minpeng Jung, Tzzy-Ping Ming, Dong Tianjin Univ Acad Med Engn & Translat Med Tianjin Peoples R China Tianjin Univ Coll Precis Instruments & Optoelect Engn Dept Biomed Engn Tianjin Peoples R China Univ Calif San Diego Swartz Ctr Computat Neurosci San Diego CA 92103 USA

A brain-computer interface (BCI) can connect humans and machines directly and has achieved successful applications in the past few decades. Many new BCI paradigms and algorithms have been developed in recent years. Therefore, it is necessary to review new progress in BCIs. This paper summarizes progress for EEG-based BCIs from the perspective of encoding paradigms and decoding algorithms, which are two key elements of BCI systems. Encoding paradigms are grouped by their underlying neural meachanisms, namely sensory- and motor-related, vision-related, cognition-related and hybrid paradigms. decoding algorithms are reviewed in four categories, namely decomposition algorithms, Riemannian geometry, deep learning and transfer learning. This review will provide a comprehensive overview of both modern primary paradigms and algorithms, making it helpful for those who are developing BCI systems.

关键词： EEG BCI Encoding paradigms decoding algorithms Review

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decoding of linear codes over Galois rings

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IEEE TRANSACTIONS ON INFORMATION THEORY 2001年第4期47卷 1599-1603页

作者： Babu, NS Zimmermann, KH Tech Univ Hamburg Harburg Dept Elect & Comp Engn D-21071 Hamburg Germany

In this correspondence, we present a method for decoding an arbitrary linear code over a Galois ring R by a process of lifting decoding algorithms for a family of linear codes over a finite field K: forming an alpha -element chain, where K: is the quotient field of a and a has characteristic p(alpha). As a new result, this method also works for linear codes over R which are nonfree R-modules.

关键词： decoding algorithms Galois rings linear codes quaternary codes

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Taste Quality decoding Parallels Taste Sensations

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CURRENT BIOLOGY 2015年第7期25卷 890-896页

作者： Crouzet, Sebastien M. Busch, Niko A. Ohla, Kathrin Charite Inst Med Psychol D-10117 Berlin Germany Humboldt Univ Berlin Sch Mind & Brain D-10099 Berlin Germany German Inst Human Nutr Potsdam Rehbrucke Psychophysiol Food Percept D-14558 Nuthetal Germany

In most species, the sense of taste is key in the distinction of potentially nutritious and harmful food constituents and thereby in the acceptance (or rejection) of food. Taste quality is encoded by specialized receptors on the tongue, which detect chemicals corresponding to each of the basic tastes (sweet, salty, sour, bitter, and savory [1]), before taste quality information is transmitted via segregated neuronal fibers [2], distributed coding across neuronal fibers [3], or dynamic firing patterns [4] to the gustatory cortex in the insula. In rodents, both hardwired coding by labeled lines [2] and flexible, learning-dependent representations [5] and broadly tuned neurons [6] seem to coexist. It is currently unknown how, when, and where taste quality representations are established in the cortex and whether these representations are used for perceptual decisions. Here, we show that neuronal response patterns allow to decode which of four tastants (salty, sweet, sour, and bitter) participants tasted in a given trial by using time-resolved multivariate pattern analyses of large-scale electrophysiological brain responses. The onset of this prediction coincided with the earliest taste-evoked responses originating from the insula and opercular cortices, indicating that quality is among the first attributes of a taste represented in the central gustatory system. These response patterns correlated with perceptual decisions of taste quality: tastes that participants discriminated less accurately also evoked less discriminated brain response patterns. The results therefore provide the first evidence for a link between taste-related decision-making and the predictive value of these brain response patterns.

关键词： TASTE PATTERN perception ELECTROPHYSIOLOGY CONFIDENCE intervals decoding algorithms PSYCHOLOGICAL aspects

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An Improved decoding Algorithm for Finite-Geometry LDPC Codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2009年第2期57卷 302-306页

作者： Ngatched, Telex Magloire Nkouatchah Takawira, Fambirai Bossert, Martin Univ KwaZulu Natal Sch Elect Elect & Comp Engn ZA-4041 Durban South Africa Univ Ulm Dept Telecommun & Appl Informat Theory D-89081 Ulm Germany

In this letter, an improved bit-flipping decoding algorithm for high-rate finite-geometry low-density parity-check (FG-LDPC) codes is proposed. Both improvement in performance and reduction in decoding delay are observed by flipping multiple bits in each iteration. Our studies show that the proposed algorithm achieves an appealing tradeoff between performance and complexity for FG-LDPC codes.

关键词： Belief propagation algorithm bit-flipping (BF) decoding algorithms low-density parity-check (LDPC) codes

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Fast decoding for RaptorQ codes using matrix dimensionality reduction

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ELECTRONICS LETTERS 2014年第16期50卷 1139-1140页

作者： Guo, Xiao Zhang, Geng-Xin Tian, Chang Zhang, Lei Zhao, Weng-Dong PLA Univ Sci & Technol Coll Commun Engn Nanjing 210007 Jiangsu Peoples R China

A very fast decoding algorithm using matrix dimensionality reduction for RaptorQ codes is proposed. The algorithm exploits a pre-calculated inverse matrix to achieve dimensionality reduction for the received code constraint matrix. As a result, the decoding complexity is decreased significantly, whereas the failure-overhead curve is still identical to that of conventional approaches. Simulations show that the decoding speed of the proposed algorithm can be as fast as 17.5 times the state-of-the-art algorithm when the erasure probability is relatively low.

关键词： decoding algorithms MATRICES CURVES GEOMETRY ITERATIVE decoding

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Extracting multidimensional stimulus-response correlations using hybrid encoding-decoding of neural activity

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NEUROIMAGE 2018年第PartA期180卷 134-146页

作者： Dmochowski, Jacek P. Ki, Jason J. DeGuzman, Paul Sajda, Paul Parra, Lucas C. CUNY Dept Biomed Engn New York NY 10031 USA Neuromatters LLC New York NY 10038 USA Columbia Univ Dept Biomed Engn New York NY 10027 USA

In neuroscience, stimulus-response relationships have traditionally been analyzed using either encoding or decoding models. Here we propose a hybrid approach that decomposes neural activity into multiple components, each representing a portion of the stimulus. The technique is implemented via canonical correlation analysis (CCA) by temporally filtering the stimulus (encoding) and spatially filtering the neural responses (decoding) such that the resulting components are maximally correlated. In contrast to existing methods, this approach recovers multiple correlated stimulus-response pairs, and thus affords a richer, multidimensional analysis of neural representations. We first validated the technique's ability to recover multiple stimulus-driven components using electroencephalographic (EEG) data simulated with a finite element model of the head. We then applied the technique to real EEG responses to auditory and audiovisual narratives experienced identically across subjects, as well as uniquely experienced video game play. During narratives, both auditory and visual stimulus-response correlations (SRC) were modulated by attention and tracked inter-subject correlations. During video game play, SRC varied with game difficulty and the presence of a dual task. Interestingly, the strongest component extracted for visual and auditory features of film clips had nearly identical spatial distributions, suggesting that the predominant encephalographic response to naturalistic stimuli is supramodal. The diversity of these findings demonstrates the utility of measuring multidimensional SRC via hybrid encoding-decoding.

关键词： STIMULUS & response (Psychology) NEURAL physiology NEUROSCIENCES ELECTROENCEPHALOGRAPHY decoding algorithms

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On uniqueness of alphabetic decoding

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DISCRETE MATHEMATICS AND APPLICATIONS 2012年第5-6期22卷 571-581页

作者： Dergach, P. S.

We establish the algorithmic solvability of the problem of uniqueness of alphabetic decoding of regular texts.

关键词： decoding algorithms PROBLEM solving UNIQUENESS (Mathematics) MATHEMATICAL analysis MATHEMATICAL programming

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Clusterless decoding of Position from Multiunit Activity Using a Marked Point Process Filter

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NEURAL COMPUTATION 2015年第7期27卷 1438-1460页

作者： Deng, Xinyi Liu, Daniel F. Kay, Kenneth Frank, Loren M. Eden, Uri T. Boston Univ Dept Math & Stat Boston MA 02215 USA Univ Calif San Francisco Grad Program Bioengn Univ Calif Berkeley San Francisco CA 94158 USA Univ Calif San Francisco Dept Physiol San Francisco CA 94158 USA

Point process filters have been applied successfully to decode neural signals and track neural dynamics. Traditionally these methods assume that multiunit spiking activity has already been correctly spike-sorted. As a result, these methods are not appropriate for situations where sorting cannot be performed with high precision, such as real-time decoding for brain-computer interfaces. Because the unsupervised spike-sorting problem remains unsolved, we took an alternative approach that takes advantage of recent insights into clusterless decoding. Here we present a new point process decoding algorithm that does not require multiunit signals to be sorted into individual units. We use the theory of marked point processes to construct a function that characterizes the relationship between a covariate of interest (in this case, the location of a rat on a track) and features of the spike waveforms. In our example, we use tetrode recordings, and the marks represent a four-dimensional vector of the maximum amplitudes of the spike waveform on each of the four electrodes. In general, the marks may represent any features of the spike waveform. We then use Bayes's rule to estimate spatial location from hippocampal neural activity. We validate our approach with a simulation study and experimental data recorded in the hippocampus of a rat moving through a linear environment. Our decoding algorithm accurately reconstructs the rat's position from unsorted multiunit spiking activity. We then compare the quality of our decoding algorithm to that of a traditional spike-sorting and decoding algorithm. Our analyses show that the proposed decoding algorithm performs equivalent to or better than algorithms based on sorted single-unit activity. These results provide a path toward accurate real-time decoding of spiking patterns that could be used to carry out content-specific manipulations of population activity in hippocampus or elsewhere in the brain.

关键词： NEUROPHYSIOLOGY POINT processes decoding algorithms CLUSTER analysis (Statistics) COMPUTER simulation HIPPOCAMPUS (Brain)

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Reduced complexity Log-MAP algorithm with Jensen inequality based non-recursive max* operator for turbo TCM decoding

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EURASIP JOURNAL ON WIRELESS COMMUNICATIONS AND NETWORKING 2013年第1期000卷 1-11页

作者： Sybis, Michal Tyczka, Piotr Poznan Univ Tech Chair Wireless Commun PL-60965 Poznan Poland

In this paper, a reduced complexity Log-MAP algorithm based on a non-recursive approximation of the max* operator is presented and studied for turbo trellis-coded modulation (TTCM) systems. In the algorithm, denoted as AvN Log-MAP, the max* operation is generalized and performed on n >= 2 arguments. The approximation is derived from the Jensen inequality. The non-recursive form of the max* calculations allows to achieve significant reduction in the decoding effort in comparison to the conventional Log-MAP algorithm. Bit-error rate performance simulation results for serial and parallel TTCM schemes in the additive white Gaussian noise and uncorrelated Rayleigh fading channels show that the AvN Log-MAP algorithm performs close to the Log-MAP. Performance and complexity comparisons of the AvN Log-MAP algorithm against the Log-MAP and several relevant reduced complexity turbo decoding algorithms proposed in the literature reveal, that it offers favorable low computational effort for the price of small performance degradation.

关键词： decoding algorithms Log-MAP algorithm Reduced-complexity algorithms max* operator Jacobian logarithm Turbo TCM

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