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On the complexity of some cryptographic problems based on the general decoding problem

IEEE TRANSACTIONS ON INFORMATION THEORY 2002年第10期48卷 2669-2678页

作者： Johansson, T Jönsson, F Lund Univ Dept Informat Technol S-22100 Lund Sweden

A new probabilistic algorithm for decoding one received word from a set of many given received words, into a codeword such that the Hamming distance between the received word and the codeword is at most t, is proposed. The new algorithm is applicable to several cryptographic problems, such as the Stern identification scheme, the McEliece public-key cryptosystem, and in correlation attacks on stream ciphers. When applicable, it runs significantly faster than previous algorithms used for attacks on these cryptosystems.

关键词： complexity correlation attack decoding algorithms McEliece cryptosystem Stern identification system

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On acceptance criterion for efficient successive errors-and-erasures decoding of Reed-Solomon and BCH codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 1997年第5期43卷 1477-1488页

作者： Kamiya, N C&C Research Laboratories NEC Corporation Limited Kawasaki Japan

We describe an efficient algorithm for successive errors-and-erasures decoding of BCH codes, The decoding algorithm consists of finding all necessary error locator polynomials and errata evaluator polynomials, choosing the most appropriate error locator polynomial and errata evaluator polynomial, using these two polynomials to compute a candidate codeword for the decoder output, and testing the candidate for optimality,ia an originally developed acceptance criterion, Even in the most stringent case possible, the acceptance criterion is only a little more stringent than Forney's criterion for GMD decoding, We present simulation results on the error performance of our decoding algorithm for binary antipodal signals over an AWGN channel and a Rayleigh fading channel, The number of calculations of elements in a finite field that are required by our algorithm is only slightly greater than that required by hard-decision decoding, while error performance is almost as good as that achieved with GMD decoding, The presented algorithm is also applicable to efficient decoding of product RS codes.

关键词： decoding algorithms decoding complexity generalized minimum-distance decoding Reed-Solomon codes soft decisions successive errors-and-erasures decoding

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Novel binary tree Huffman decoding algorithm and field programmable gate array implementation for terrestrial-digital multimedia broadcasting mobile handheld

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IET SCIENCE MEASUREMENT & TECHNOLOGY 2012年第6期6卷 527-532页

作者： Beak, S. Van Hieu, B. Lee, H. Choi, S. Kim, I. Lee, K. Lee, Y. Jeong, T. Myongji Univ Dept Elect Engn Yongin South Korea Korea Elect Telecommun Inst Seoul South Korea

Recent mobile devices, which adopted Eureka-147, terrestrial-digital multimedia broadcasting (T-DMB) systems, are developed as integrated circuit. As a result, the space of memory expands hardly on mobile handheld. Therefore most mobile handheld must operate a lot of application on limited memory. To solve the problem, most of the mobile devices use some kind of compression algorithms to overcome the memory shortage. Among such algorithms, Huffman algorithm is most widely used. In this study, the authors present a novel binary tree expression of the Huffman decoding algorithm which reduces the memory use approximately by 50% and increases the decoding speed up to 30%. The authors experiment the decoding speed on an evaluation kit (SMDK 6400), which is a T-DMB mobile handheld with an advanced risk machine processor. Later to enhance the decoding speed, the authors present an optimum Huffman decoder based on hardware implementation.

关键词： decoding algorithms FIELD programmable gate arrays MULTIMEDIA systems MOBILE apps INTEGRATED circuits PROBLEM solving

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decoding neuronal diversity in the developing cerebral cortex: from single cells to functional networks

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CURRENT OPINION IN NEUROBIOLOGY 2018年 53卷 146-155页

作者： Mancinelli, Sara Lodato, Simona IRCCS Humanitas Clin & Res Ctr Via Manzoni 56 I-20089 Rozzano Milan Italy Humanitas Univ Dept Biomed Sci Via Rita Levi Montalcini 4 I-20090 Pieve Emanuele Milan Italy

The neocortex is by far one of the most complex regions of the mammalian brain, characterized by an extraordinary diversity of neuronal and non-neuronal cell types, whose coordinated development and function guarantee the execution of high order cognitive, sensory, and motor behaviours. decoding its heterogeneity and understanding the molecular strategies upon which the cerebral cortex is built during development have been at the core of neuroscientists' work for decades. Here, we will focus on the current classification of neuronal types (both excitatory and inhibitory) of the neocortex in light of the insights provided by recent single-cell omit technologies, which have offered with unprecedented resolution an extended framework to interpret cortical diversity and its developmental origin. We will cover the impact of neuronal subtype identity on generating specific neuronal networks (neuron-to-neuron interaction), as well as their effect on the development of the non-neuronal populations in the cerebral cortex.

关键词： decoding algorithms BIODIVERSITY CEREBRAL cortex TRANSCRIPTOMES EXCITATORY amino acids

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Noise-Robust Speech Recognition Through Auditory Feature Detection and Spike Sequence decoding

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NEURAL COMPUTATION 2014年第3期26卷 523-556页

作者： Schafer, Phillip B. Jin, Dezhe Z. Penn State Univ Dept Phys University Pk PA 16802 USA Penn State Univ Ctr Neural Engn University Pk PA 16802 USA

Speech recognition in noisy conditions is a major challenge for computer systems, but the human brain performs it routinely and accurately. Automatic speech recognition (ASR) systems that are inspired by neuroscience can potentially bridge the performance gap between humans and machines. We present a system for noise-robust isolated word recognition that works by decoding sequences of spikes from a population of simulated auditory feature-detecting neurons. Each neuron is trained to respond selectively to a brief spectrotemporal pattern, or feature, drawn from the simulated auditory nerve response to speech. The neural population conveys the time-dependent structure of a sound by its sequence of spikes. We compare two methods for decoding the spike sequencesone using a hidden Markov model-based recognizer, the other using a novel template-based recognition scheme. In the latter case, words are recognized by comparing their spike sequences to template sequences obtained from clean training data, using a similarity measure based on the length of the longest common sub-sequence. Using isolated spoken digits from the AURORA-2 database, we show that our combined system outperforms a state-of-the-art robust speech recognizer at low signal-to-noise ratios. Both the spike-based encoding scheme and the template-based decoding offer gains in noise robustness over traditional speech recognition methods. Our system highlights potential advantages of spike-based acoustic coding and provides a biologically motivated framework for robust ASR development.

关键词： AUTOMATIC speech recognition FEATURE extraction (Data processing) decoding algorithms ROBUST control HUMAN-computer interaction WORD recognition

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A Novel Nonparametric Approach for Neural Encoding and decoding Models of Multimodal Receptive Fields

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NEURAL COMPUTATION 2016年第7期28卷 1356-1387页

作者： Agarwal, Rahul Chen, Zhe Kloosterman, Fabian Wilson, Matthew A. Sarma, Sridevi V. Johns Hopkins Univ Dept Biomed Engn Baltimore MD 21218 USA NYU Sch Med Dept Psychiat New York NY 10016 USA NYU Sch Med Dept Neurosci & Physiol New York NY 10016 USA Neuroelect Res Flanders Leuven Belgium IMEC Leuven Belgium Katholieke Univ Leuven Brain & Cognit Res Unit B-3000 Leuven Belgium MIT Picower Inst Learning & Memory 77 Massachusetts Ave Cambridge MA 02139 USA

Pyramidal neurons recorded from the rat hippocampus and entorhinal cortex, such as place and grid cells, have diverse receptive fields, which are either unimodal or multimodal. Spiking activity from these cells encodes information about the spatial position of a freely foraging rat. At fine timescales, a neuron's spike activity also depends significantly on its own spike history. However, due to limitations of current parametric modeling approaches, it remains a challenge to estimate complex, multimodal neuronal receptive fields while incorporating spike history dependence. Furthermore, efforts to decode the rat's trajectory in one- or two-dimensional space from hippocampal ensemble spiking activity have mainly focused on spike history-independent neuronal encoding models. In this letter, we address these two important issues by extending a recently introduced nonparametric neural encoding framework that allows modeling both complex spatial receptive fields and spike history dependencies. Using this extended nonparametric approach, we develop novel algorithms for decoding a rat's trajectory based on recordings of hippocampal place cells and entorhinal grid cells. Results show that both encoding and decoding models derived from our new method performed significantly better than state-of-the-art encoding and decoding models on 6 minutes of test data. In addition, our model's performance remains invariant to the apparent modality of the neuron's receptive field.

关键词： NONPARAMETRIC estimation NEURAL codes ENCODING decoding algorithms PYRAMIDAL neurons PARAMETRIC modeling ACTION potentials (Electrophysiology)

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Suboptimal soft-decision decoding for some RS-codes

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ELECTRONICS LETTERS 1998年第10期34卷 983-984页

作者： Wesemeyer, S Sweeney, P Univ Surrey Ctr Commun Syst Res Guildford GU2 5XH Surrey England

A novel soft-decision algorithm is presented for Reed-Solomon (RS) codes, based on the reordering of the symbols of the received word according to some measure of reliability. The simulation results show that improvements in coding gain of > 1 dB are possible when compared to similar decoding algorithms using unsorted received words.

关键词： decoding algorithms Reed-Solomon codes Codes suboptimal soft-decision decoding reliability symbol reordering RS-codes decoding coding gain

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Fast decoding of the p-ary first-order Reed-Muller codes based on Jacket transform

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2008年第3期E91A卷 901-904页

作者： Lee, Moon Ho Borissov, Yuri L. Chonbuk Natl Univ Inst Informat & Commun Jeonju 561756 South Korea Bulgarian Acad Sci Inst Math & Informat BU-1113 Sofia Bulgaria

We propose a fast decoding algorithm for the p-ary first-order Reed-Muller code guaranteeing correction of up to left perpendicularn/4 sin(p-1/2p)right perpendicular errors and having complexity proportional to n log n, where n = p(m) is the code length and p is an odd prime. This algorithm is an extension in the complex domain of the fast Hadamard transform decoding algorithm applicable to the binary case.

关键词： p-ary first-order Reed-Muller codes decoding algorithms Jacket matrix

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On decoding Grid Cell Population Codes Using Approximate Belief Propagation

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NEURAL COMPUTATION 2017年第3期29卷 716-734页

作者： Yoo, Yongseok Kim, Woori Incheon Natl Univ Dept Elect Engn Incheon 22012 South Korea Chonnam Natl Univ Dept Special Educ Jeonnam 59626 South Korea

Neural systems are inherently noisy. One well-studied example of a noise reduction mechanism in the brain is the population code, where representing a variable with multiple neurons allows the encoded variable to be recovered with fewer errors. Studies have assumed ideal observer models for decoding population codes, and the manner in which information in the neural population can be retrieved remains elusive. This letter addresses a mechanism by which realistic neural circuits can recover encoded variables. Specifically, the decoding problem of recovering a spatial location from populations of grid cells is studied using belief propagation. We extend the belief propagation decoding algorithm in two aspects. First, beliefs are approximated rather than being calculated exactly. Second, decoding noises are introduced into the decoding circuits. Numerical simulations demonstrate that beliefs can be effectively approximated by combining polynomial nonlinearities with divisive normalization. This approximate belief propagation algorithm is tolerant to decoding noises. Thus, this letter presents a realistic model for decoding neural population codes and investigates fault-tolerant information retrieval mechanisms in the brain.

关键词： GRID cells NEURONS NEURAL circuitry NEURAL networks (Neurobiology) COMPUTER simulation decoding algorithms

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Expander l₀-decoding

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APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS 2018年第3期45卷 642-667页

作者： Mendoza-Smith, Rodrigo Tanner, Jared Univ Oxford Math Inst Oxford OX2 6GG England

We introduce two new algorithms, Serial-l(0) and Parallel-l(0) for solving a large underdetermined linear system of equations y = Ax is an element of R-m when it is known that x is an element of R-n has at most k < m nonzero entries and that A is the adjacency matrix of an unbalanced left d-regular expander graph. The matrices in this class are sparse and allow a highly efficient implementation. A number of algorithms have been designed to work exclusively under this setting, composing the branch of combinatorial compressed-sensing (CCS). Serial-l(0) and Parallel-l(0) iteratively minimise parallel to y - A<(x)over cap>parallel to(0) by successfully combining two desirable features of previous CCS algorithms: the coordinate selection strategy of ER [1] for updating (x) over cap, and the parallel updating mechanism of SMP [2]. We are able to link these elements and guarantee convergence in O(dn log k) operations by introducing a randomised scaling of columns in A, with scaling chosen independent of the measured vector. We also empirically observe that the recovery properties of Serial-l(0) and Parallel-l(0) degrade gracefully as the signal is allowed to have its non-zero values chosen adversarially. Moreover, we observe Serial-l(0) and Parallel-l(0) to be able to solve large scale problems with a larger fraction of nonzeros than other algorithms when the number of measurements is substantially less than the signal length;in particular, they are able to reliably solve for a k-sparse vector x is an element of R-n from m expander measurements with n/m = 10(3) and k/m up to four times greater than what is achievable by l(1)-regularisation from dense Gaussian measurements. Additionally, due to their low computational complexity, Serial-l(0) and Parallel-l(0) are observed to be able to solve large problems sizes in substantially less time than other algorithms for compressed sensing. In particular, Parallel-l(0) is structured to take advantage of massively parallel architec

关键词： Compressed sensing Combinatorial compressed sensing decoding algorithms Dissociated signals Expander graphs

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