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Bounded-Degree Low-Rank Parity-Check Codes

IEEE TRANSACTIONS ON INFORMATION THEORY 2025年第3期71卷 1593-1612页

作者： Franch, Ermes Li, Chunlei Univ Bergen Dept Informat N-5008 Bergen Norway

Low-rank parity-check (LRPC) codes are the rank-metric analogue of low-density parity-check codes and they found important applications in code-based cryptography. In this paper we investigate a sub-family of LRPC codes, which have a parity-check matrix defined over a subspace V alpha,d = < 1, alpha, ... , alpha d-1 > Fq & subne;Fqm, where Fqm is the finite field of qm elements, alpha is an element of Fqm is an element not in any proper subfield of Fqm, and d is a positive integer significantly smaller than m. These codes are termed bounded-degree LRPC (BD-LRPC) codes. BD-LRPC codes are the same as the standard LRPC codes of density 2 when the degree d = 2, while for degree d > 2 they constitute a proper subset of LRPC codes of density d. Exploiting the structure of V alpha,d, the BD-LRPC codes of degree d can uniquely correct errors of rank weight r when n-k > r + u for certain u > 1, in contrast to the condition n - k > dr required for the standard LRPC codes. This underscores the superior decoding capability of the BD-LRPC codes. Moreover, as the code length n-+ infinity, when n/m-+ 0, the BD-LRPC codes with a code rate of R = k/n can be uniquely decodable with radius rho = r/n approaching the Singleton bound 1 - R by letting & varepsilon;= u/n-+ 0;and when n/m is a constant, the BD-LRPC codes can have unique decoding radius rho = 1-R-& varepsilon;for a small & varepsilon;, allowing for rho> (1-R)/2 with properly chosen parameters. This superior decoding capability is theoretically proved for the case d = 2 and confirmed by experimental results for d > 2.

关键词： Codes decoding Measurement Vectors Cryptography Parity check codes Finite element analysis Standards Reed-Solomon codes probabilistic logic Low-rank parity-check (LRPC) codes probabilistic decoding decoding radius Singleton bound Gaussian binomial coefficient Ferrers diagram

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Performance Evaluation of Finite Sparse Signals for Compressed Sensing Frameworks

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IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS 2018年第2期E101D卷 531-534页

作者： Seong, Jin-Taek Honam Univ Dept Informat & Commun Engn Gwangju South Korea

In this paper, we consider to develop a recovery algorithm of a sparse signal for a compressed sensing (CS) framework over finite fields. A basic framework of CS for discrete signals rather than continuous signals is established from the linear measurement step to the reconstruction. With predetermined priori distribution of a sparse signal, we reconstruct it by using a message passing algorithm, and evaluate the performance obtained from simulation. We compare our simulation results with the theoretic bounds obtained from probability analysis.

关键词： compressed sensing finite fields signal recovery probabilistic decoding

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Sparse Output Coding for Scalable Visual Recognition

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INTERNATIONAL JOURNAL OF COMPUTER VISION 2016年第1期119卷 60-75页

作者： Zhao, Bin Xing, Eric P. Carnegie Mellon Univ Sch Comp Sci Pittsburgh PA 15213 USA

Many vision tasks require a multi-class classifier to discriminate multiple categories, on the order of hundreds or thousands. In this paper, we propose sparse output coding, a principled way for large-scale multi-class classification, by turning high-cardinality multi-class categorization into a bit-by-bit decoding problem. Specifically, sparse output coding is composed of two steps: efficient coding matrix learning with scalability to thousands of classes, and probabilistic decoding. Empirical results on object recognition and scene classification demonstrate the effectiveness of our proposed approach.

关键词： Scalable classification Output coding probabilistic decoding Object recognition Scene recognition

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A probabilistic decoding Approach to a Neural Prosthesis for Speech

A Probabilistic Decoding Approach to a Neural Prosthesis for...

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4th International Conference on Bioinformatics and Biomedical Engineering (iCBBE)

作者： Matthews, Brett Kim, Jonathan Brumberg, Jonathan S. Clements, Mark Georgia Inst Technol Sch Elect & Comp Engn Atlanta GA 30332 USA Boston Univ Dept Cognit & Neural Syst Boston MA 02215 USA

ISBN: (纸本)9781424447138

Neural prosthetic systems for motor control and communication have produced striking results in recent studies with non-human primates and human volunteers. We describe a new approach in our ongoing work toward developing an intracortical neural prosthesis for speech restoration with a 26 year old human volunteer with tetraplegia (including loss of vocal and facial muscle control). We propose to use hidden Markov models (HMMs) to decode neural firing activity in speech motor cortex. We show how classical and recent approaches to automatic speech recognition (ASR) apply directly to the decoding stage of a neural prosthesis. We outline a series of experiments in collecting cortical neural firing data from our human volunteer, and discuss important challenges and considerations in implementing an HMM framework for a neural speech prosthesis.

关键词： Neural Prostheses Human Volunteers Speech probabilistic decoding Facial Muscles Quadriplegia Primary Motor Cortex decoding

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Sparse Output Coding for Large-Scale Visual Recognition

Sparse Output Coding for Large-Scale Visual Recognition

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IEEE Conference on Computer Vision and Pattern Recognition

作者： Bin Zhao Eric P. Xing School of Computer Science Carnegie Mellon University

ISBN: (纸本)9781467364102

关键词： multi-class object recognition Scalability probabilistic decoding Phyla Output

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On the Relationship Between Belief Propagation decoding and Joint Maximum Likelihood Detection

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IEEE TRANSACTIONS ON COMMUNICATIONS 2010年第10期58卷 2753-2758页

作者： Walsh, John MacLaren Regalia, Phillip Allan Drexel Univ Philadelphia PA 19104 USA Catholic Univ Amer Washington DC 20064 USA

Belief propagation, via a novel reinterpretation of the Bethe free energy's pseudo-dual, is shown to be related to a novel relaxation of maximum likelihood detection via a constrained optimization. The conventional maximum likelihood detection falls out for a zero constraint, and belief propagation's fixed points are obtained for other constraint values.

关键词： Belief propagation factor graphs probabilistic decoding turbo decoding iterative decoding

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PERFORMANCE ANALYSIS AND OPTIMIZATION FOR ARQ DECODE-AND-FORWARD RELAYING PROTOCOL IN FAST FADING CHANNELS

PERFORMANCE ANALYSIS AND OPTIMIZATION FOR ARQ DECODE-AND-FOR...

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IEEE International Conference on Acoustics, Speech, and Signal Processing

作者： Sangkook Lee Weifeng Su Stella Batalama John D. Matyjas State University of New York at Buffalo Dept. of Electrical Engineering NY 14260 Air Force Research Laboratory/RIGE Rome NY 13441

ISBN: (纸本)9781424442959

In this paper, a new analytical approach is developed for the evaluation of the outage probability of decode-and-forward (DF) automatic-repeat-request (ARQ) relaying under packet-rate fading (fast fading) channels. Based on this approach, a closed-form asymptotically tight (as SNR -> infinity) approximation of the outage probability is derived, and the diversity order of the DF cooperative ARQ relay scheme is shown to be equal to 2L - 1, where L is the maximum number of ARQ retransmissions. The closed-form expression clearly shows that the achieved diversity is partially due to the DF cooperative relaying and partially due to the fast fading nature of the channels (temporal diversity). Numerical and simulation studies illustrate the theoretical developments.

关键词： Automatic-repeat-request (ARQ) protocol co-operative decode-and-forward relaying outage probability Automatic repeat request fading color fast fading channel DEUTERIUM FLUORIDES probabilistic decoding protocols

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Reliability-based soft-decision decoding with multiple biases

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IEEE TRANSACTIONS ON INFORMATION THEORY 2007年第1期53卷 105-120页

作者： Jin, Wenyi Fossorier, Marc P. C. Univ Hawaii Manoa Dept Elect Engn Honolulu HI 96822 USA

In this paper, a new reliability-based soft-decision decoding algorithm is presented. This algorithm repeatedly uses biased reliability values to construct the most-reliable-basis (MRB). As a result, this new method makes use of multiple information sets in a stochastic way. Compared to previously proposed competitive approaches, this new method produces a more efficient MRB reprocessing type algorithm to achieve near maximum-likelihood decoding (MLD) performance with a proper choice of the bias value. It can be combined with any MRB reprocessing type algorithm and in each case, a tight performance analysis can be derived.

关键词： linear block codes list decoding maximum-likelihood decoding order statistics probabilistic decoding Reed-Solomon codes

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Sparse-graph codes for quantum error correction

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IEEE TRANSACTIONS ON INFORMATION THEORY 2004年第10期50卷 2315-2330页

作者： MacKay, DJC Mitchison, G McFadden, PL Cavevdish Lab Dept Phys Cambridge CB3 0HE England MRC Mol Biol Lab Cambridge CB2 2QH England Dept Appl Math & Theoret Phys Cambridge CB3 0WA England

Sparse-graph codes appropriate for use in quantum error-correction are presented. Quantum error-correcting codes based on sparse graphs are of interest for three reasons. First, the best codes currently known for classical channels are based on sparse graphs. Second, sparse-graph codes keep the number of quantum interactions associated with the quantum error-correction process small: a constant number per quantum bit, independent of the block length. Third, sparse-graph codes often offer great flexibility with respect to block length and rate. We believe some of the codes we present are unsurpassed by previously published quantum error-correcting codes.

关键词： error-correction codes probabilistic decoding quantum error correction

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Reliability-based soft-decision decoding with iterative information set reduction

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IEEE TRANSACTIONS ON INFORMATION THEORY 2002年第12期48卷 3101-3106页

作者： Fossorier, MPC Univ Hawaii Dept Elect Engn Honolulu HI 96822 USA

In this correspondence, the reliability-based decoding approach using the reprocessing of the most reliable information set only is extended into the iterative reprocessing of several information sets. At the end of each information set reprocessing, some information bits are delivered by the decoder. Consequently, information sets with decreasing cardinality values are considered at each iteration. A tight upper bound on the error performance achieved by this new method is derived. Compared to previously proposed competitive approaches, this new method reduces the number of candidate codewords needed to achieve practically optimum decoding. Importantly, it also preserves the very simple structured implementation of the order statistic decoding.

关键词： block codes information set decoding maximum-likelihood decoding (MLD) order statistic decoding probabilistic decoding soft-decision decoding

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