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Min-Sum Algorithm Using Multi-Edge-Type Normalized Scheme for ATSC 3.0 LDPC Decoders

IEEE TRANSACTIONS ON BROADCASTING 2020年第3期66卷 729-736页

作者： Gao, Na Xu, Yin He, Dazhi Park, Sung-Ik Hong, Hanjiang Ju, Hao Chen, Changwen Zhang, Wenjun Shanghai Jiao Tong Univ Sch Elect Engn Shanghai 200240 Peoples R China Elect & Telecommun Res Inst Broadcasting Syst Res Dept Daejeon 34129 South Korea SUNY Buffalo Dept Comp Sci & Engn Buffalo NY 14260 USA

To offer commercial LDPC decoders with better performance, in this paper, multi-edge-type (MET) normalized scheme is proposed to improve the performance of traditional min-sum algorithm (MSA) and its modified versions. With respect to sum-product algorithm (SPA), we firstly analyze and find out that the degradations of convergence in different edge types are distinct in MSA theoretically. To compensate the different degradations above, proposed MET-normalized scheme is used in normalized min-sum algorithm (MET-NMSA). In addition, MET-based density evolution (MET-DE) is also presented to search optimized MET-scaling factors for MET-NMSA. To further verify the validity of MET-normalized scheme, Advanced Television Systems Committee (ATSC) 3.0 LDPC codes are used to evaluate MET-NMSA in comparison with the conventional algorithms, i.e., normalized min-sum algorithm (NMSA), offset min-sum algorithm (OMSA) and variable-scaling normalized min-sum algorithm (VS-NMSA). Extensive simulation results show that MET-NMSA for ATSC 3.0 LDPC decoders has at most 1.53dB, 0.21dB and 0.35dB gain over NMSA, OMSA and VS-NMSA respectively when frame error rate (FER) is at 10(-4) level over additive white Gaussian noise (AWGN) channels using QPSK modulation.

关键词： decoding Phase change materials Manganese Iterative decoding Convergence Approximation algorithms ATSC 3 0 LDPC codes MET-normalized scheme decoding algorithms density evolution

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Algebraic-geometry codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 1998年第6期44卷 2596-2618页

作者： Blake, I Heegard, C Hoholdt, T Wei, V Hewlett Packard Labs Palo Alto CA 94304 USA Cornell Univ Sch Elect Engn Ithaca NY 14853 USA Tech Univ Denmark Inst Math DK-2800 Lyngby Denmark Chinese Univ Hong Kong Dept Informat Engn Shatin New Territory Peoples R China

The theory of error-correcting codes derived from curves in an algebraic geometry was initiated by the work of Goppa as generalizations of Bose-Chaudhuri-Hocquenghem (BCH), Reed-Solomon (RS), and Goppa codes. The development of the theory has received intense consideration since that time and the purpose of the paper is to review this work. Elements of the theory of algebraic curves, at a level sufficient to understand the code constructions and decoding algorithms, are introduced. Code constructions from particular classes of curves, including the Klein quartic, elliptic, and hyperelliptic curves, and Hermitian curves, are presented, decoding algorithms for these classes of codes, and others, are considered. The construction of classes of asymptotically good codes using modular curves is also discussed.

关键词： algebraic curves algebraic-geometry codes asymptotically good codes decoding algorithms

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Approximately even partition algorithm for coding the Hilbert curve of arbitrary-sized image

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IET IMAGE PROCESSING 2012年第6期6卷 746-755页

作者： Wu, C-C. Chang, Y-I. Natl Sun Yat Sen Univ Dept Comp Sci & Engn Kaohsiung 80424 Taiwan

The Hilbert curve is one of space filling curves and it requires that the region is of size 2(k) x 2(k), where k is an element of N. This study relaxes this constraint and generates a pseudo-Hilbert curve of arbitrary dimension. The intuitive method such as Chung et al.'s algorithm is to use Hilbert curves in the decomposed areas directly and then have them connected. However, they must generate a sequence of the scanned quadrants additionally before encoding and decoding the Hilbert order of one pixel. In this study, by using the approximately even partition approach, the authors propose a new Hilbert curve, the Hilbert* curve, which permits any square regions. Experimental results show that the clustering property of the Hilbert* curve is similar to that of the standard Hilbert curve. Next, the authors also propose encoding/decoding algorithms for the Hilbert* curves. Since the authors do not need to additionally generate and scan the sequence of quadrants, the proposed algorithm outperforms Chung et al.'s algorithms for the square region. Then, the authors apply the Hilbert* curves in Chung et al.'s algorithms for the Hilbert curve of arbitrary dimension and experimental results show that the proposed encoding/decoding algorithms out perform the Chung et al.'s approach.

关键词： space filling curves Computer vision and image processing techniques scanned quadrants Image and video coding decoding algorithms arbitrary dimension image coding pseudoHilbert curve Hilbert transforms arbitrary sized image Integral transforms in numerical analysis approximately even partition algorithm decoding clustering property

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On Using Noisy Feedback in a Gaussian Channel

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PROBLEMS OF INFORMATION TRANSMISSION 2014年第3期50卷 217-231页

作者： Burnashev, M. V. Yamamoto, H. Russian Acad Sci Kharkevich Inst Informat Transmiss Problems Moscow Russia Univ Tokyo Sch Frontier Sci Tokyo 1138654 Japan

For information transmission, a discrete-time channel with independent additive Gaussian noise is used. There is also another channel with independent additive Gaussian noise (the feedback channel), and the transmitter observes all outputs of the forward channel without delay via that channel. Transmission of nonexponentially many messages is considered (i.e., the transmission rate is zero), and the achievable decoding error exponent for such a combination of channels is investigated. The transmission method strengthens the method previously used by the authors for the BSC and Gaussian channels. In particular, for small feedback noise, this yields a gain of 33.3% (instead of 23.6% earlier in the similar case of a Gaussian channel).

关键词： GAUSSIAN channels GAUSSIAN processes DISCRETE-time systems RANDOM noise theory decoding algorithms

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Bias, optimal linear estimation, and the differences between open-loop simulation and closed-loop performance of spiking-based brain-computer interface algorithms

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NEURAL NETWORKS 2009年第9期22卷 1203-1213页

作者： Chase, Steven M. Schwartz, Andrew B. Kass, Robert E. Carnegie Mellon Univ Dept Stat Pittsburgh PA 15203 USA Univ Pittsburgh Dept Neurobiol Pittsburgh PA 15260 USA Univ Pittsburgh Ctr Neural Basis Cognit Pittsburgh PA 15260 USA

The activity of dozens of simultaneously recorded neurons can be used to control the movement of a robotic arm or a Cursor on a computer screen This motor neural prosthetic technology has Spurred an increased interest in the algorithms by which motor intention can be inferred. The simplest of these algorithms is the population vector algorithm (PVA). where the activity of each cell is used to weight a vector pointing in that neuron's preferred direction Off-line, it is possible to show that more complicated algorithms, Such as the optimal linear estimator (OLE). can yield substantial improvements in the accuracy of reconstructed hand movements over the PVA We call this open-loop performance In contrast, this performance difference may not be present in closed-loop, on-line control The obvious difference between open and closed-loop control is the ability to adapt to the specifics of the decoder in use at the time In order to predict performance gains that an algorithm may yield in closed-loop control. it is necessary to build a model that captures aspects of this adaptation process. Here we present a framework for modeling the closed-loop performance of the PVA and the OLE. Using both simulations and experiments. we show that (1) the performance gain with certain decoders can be far less extreme than predicted by off-line results, (2) that subjects are able to compensate for certain types of bias in decoders, and (3) that care must be taken to ensure that estimation error does not degrade the performance of theoretically optimal decoders. (C) 2009 Elsevier Ltd All rights reserved.

关键词： Neural prosthetics decoding algorithms Brain-machine interface

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Reed-Muller Codes: Theory and algorithms

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IEEE TRANSACTIONS ON INFORMATION THEORY 2021年第6期67卷 3251-3277页

作者： Abbe, Emmanuel Shpilka, Amir Ye, Min Ecole Polytech Fed Lausanne Math Inst CH-1015 Lausanne Switzerland Ecole Polytech Fed Lausanne Sch Comp & Commun Sci CH-1015 Lausanne Switzerland Princeton Univ Program Appl & Computat Math Princeton NJ 08544 USA Princeton Univ Dept Elect Engn Princeton NJ 08544 USA Tel Aviv Univ Blavatnik Sch Comp Sci IL-60198 Tel Aviv Israel Tsinghua Shenzhen Int Grad Sch Tsinghua Berkeley Shenzhen Inst Data Sci & Informat Technol Res Ctr Shenzhen 518055 Peoples R China

Reed-Muller (RM) codes are among the oldest, simplest and perhaps most ubiquitous family of codes. They are used in many areas of coding theory in both electrical engineering and computer science. Yet, many of their important properties are still under investigation. This paper covers some of the recent developments regarding the weight enumerator and the capacity-achieving properties of RM codes, as well as some of the algorithmic developments. In particular, the paper discusses the recent connections established between RM codes, thresholds of Boolean functions, polarization theory, hypercontractivity, and the techniques of approximating low weight codewords using lower degree polynomials (when codewords are viewed as evaluation vectors of degree r polynomials in m variables). It then overviews some of the algorithms for decoding RM codes. It covers both algorithms with provable performance guarantees for every block length, as well as algorithms with state-of-the-art performances in practical regimes, which do not perform as well for large block length. Finally, the paper concludes with a few open problems.

关键词： Reed-Muller codes Shannon capacity weight enumerator decoding algorithms polarization

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Rank subcodes in multicomponent network coding

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PROBLEMS OF INFORMATION TRANSMISSION 2013年第1期49卷 40-53页

作者： Gabidulin, E. M. Pilipchuk, N. I. State Univ Moscow Inst Phys & Technol Moscow Russia

A new class of subcodes in rank metric is proposed;based on it, multicomponent network codes are constructed. Basic properties of subspace subcodes are considered for the family of rank codes with maximum rank distance (MRD codes). It is shown that nonuniformly restricted rank subcodes reach the Singleton bound in a number of cases. For the construction of multicomponent codes, balanced incomplete block designs and matrices in row-reduced echelon form are used. A decoding algorithm for these network codes is proposed. Examples of codes with seven and thirteen components are given.

关键词： CODING theory INCOMPLETE block designs MATRICES decoding algorithms FINITE fields (Algebra) LINEAR algebra

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Energy Consumption of VLSI Decoders

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IEEE TRANSACTIONS ON INFORMATION THEORY 2015年第6期61卷 3185-3198页

作者： Blake, Christopher G. Kschischang, Frank R. Univ Toronto Dept Elect & Comp Engn Toronto ON M5S3G4 Canada

Thompson's model of very large scale integration computation relates the energy of a computation to the product of the circuit area and the number of clock cycles needed to carry out the computation. It is shown that for any sequence of increasing block-length decoder circuits implemented according to this model, if the probability of block error is asymptotically less than 1/2 then the energy of the computation scales at least as Omega(n(log n)(1/2)), and so the energy of decoding per bit must scale at least as Omega (log n)(1/2). This implies that the average energy per decoded bit must approach infinity for any sequence of decoders that approaches capacity. The analysis techniques used are then extended to show that for any sequence of increasing block-length serial decoders, if the asymptotic block error probability is less than 1/2 then the energy scales at least as fast as Omega (n log n). In a very general case that allows for the number of output pins to vary with block length, it is shown that the energy must scale as Omega (n(log n)(1/5)). A simple example is provided of a class of circuits performing low-density parity-check decoding whose energy complexity scales as O(n(2) log log n).

关键词： Channel capacity channel coding energy-efficient communication decoding algorithms

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Performance Enhancement of Optical CDMA by Differential-Phase Method for Radio-over-Fiber Transmissions

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MATHEMATICAL PROBLEMS IN ENGINEERING 2013年第1期2013卷 1-6页

作者： Cheng, Hsu-Chih Yen, Chih-Ta Ding, Ing-Jr Natl Formosa Univ Dept Electroopt Engn Huwei Township 632 Yunlin County Taiwan Natl Formosa Univ Dept Elect Engn Huwei Township 632 Yunlin County Taiwan

The study proposes the differential-phase optical code-division multiple-access (OCDMA) network for radio-over-fiber (RoF) transmissions, and the characteristics are numerically analyzed. The network coder/decoders (codecs) are structured on the basis of arrayed-waveguide-grating (AWG) routers with complementary Walsh-Hadamard (CWH) signature codes. In the proposed system, the network requires only two AWG routers to accomplish spectral encoding of radio base station (RBS) and decoding of control station for the complementary keying, thus resulting in a simpler and low cost system. Performance analyses are evaluated with the dominant noise of phase-induced intensity noise (PIIN) in spectral code OCDMA network. By the proposed AWG-based OCDMA with the differential-phase scheme, it is possible to establish interference-free and low crosstalk beat noise RoF systems.

关键词： CODE division multiple access DIFFERENTIAL phase shift keying HADAMARD codes decoding algorithms SIGNAL-to-noise ratio

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ON THE KEY EQUATION

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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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