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CONSTRUCTION OF SOME BINARY linear codeS OF MINIMUM DISTANCE 5

IEEE TRANSACTIONS ON INFORMATION THEORY 1991年第5期37卷 1429-1432页

作者： CHEN, CL IBM Corporation Poughkeepsie NY USA

A method of constructing binary linear codes is presented that have a minimum Hamming distance of five. Some efficient new codes are obtained. In particular, a (47,36,5) code is obtained that has six more information ... 详细信息

关键词： ERROR-CORRECTING code linear block code

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THE SYNDROME DISTRIBUTION OF M-BIT ERROR PATTERNS AND THE ANALYSIS OF ATM FORWARD ERROR-CORRECTION codeS

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IEEE TRANSACTIONS ON COMMUNICATIONS 1995年第2-4期43卷 1392-1399页

作者： LEI, SM Bellcore Red Bank NJ USA

The error detection and correction capability of a linear block code is usually analyzed by its minimum distance and weight distribution function. A different analysis tool, the syndrome distribution of m-bit error patterns, is introduced in this paper. Additional detailed information about the capability of a code can be obtained from the syndrome distribution, e.g., undetected percentages, miscorrected percentages, as well as the weight distribution function. A fast algorithm is provided to compute the syndrome distribution vectors of m-bit error patterns for all m. The cyclic codes defined in asynchronous transfer mode (ATM) for broadband ISDN are used as examples to show the strength of this new analysis tool. A rough, but simple, estimation of the undetected percentages is also introduced in the paper.

关键词： error model Forward error correction error correction error detection and correction linear block code Syndromes minimum distance codes

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Asynchronous secure communication scheme using a new modulation of message on optical chaos

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OPTICAL AND QUANTUM ELECTRONICS 2023年第1期55卷 1-19页

作者： Lin, Lang Li, Qiliang Xi, Xiaohu Hangzhou Dianzi Univ Sch Commun Engn Hangzhou 310018 Zhejiang Peoples R China

An asynchronous secure communication scheme of modulation of message on optical chaos, combining (6, 3) linear block codes (LBC) with majority decoding, is proposed. In this scheme, a semiconductor laser (SL) with electro-optical phase feedback is used to generate an optical chaotic carrier with high complexity. We calculate the sum of the absolute values at adjacent three moments in the chaotic sequence, and divide interval between its maximum and minimum into eight different segments, which are used as the key for generating a new chaotic sequence according to a certain rule. Introducing (6, 3) LBC to encode the message, and using dispersion-compensating fiber (DCF) to eliminate the effect of dispersion induced by single mode fiber (SMF), and then using majority decoding to demodulate the original message at receiving end, we demonstrate that the performance of the bit error rate (BER) in a channel with noise is well improved, and the distortion is greatly reduced. Moreover, our system can realize communication between transmitter and receiver without chaotic synchronization by negotiating these keys through a secret channel.

关键词： Asynchronous Secure communication Optical chaos Semiconductor laser linear block code Majority decoding

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Parity-Check Matrices Separating Erasures From Errors

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IEEE TRANSACTIONS ON INFORMATION THEORY 2013年第6期59卷 3332-3346页

作者： Abdel-Ghaffar, Khaled A. S. Weber, Jos H. Univ Calif Davis Dept Elect & Comp Engn Davis CA 95616 USA Delft Univ Technol NL-2628 CD Delft Netherlands

Most decoding algorithms of linear codes, in general, are designed to correct or detect errors. However, many channels cause erasures in addition to errors. In principle, decoding over such channels can be accomplished by deleting the erased symbols and decoding the resulting vector with respect to a punctured code. For any given linear code and any given maximum number of correctable erasures, parity-check matrices are introduced that yield parity-check equations which do not check any of the erased symbols and which are sufficient to characterize all punctured codes corresponding to this maximum number of erasures. These matrices allow for the separation of erasures from errors to facilitate decoding. Several constructions of such separating parity-check matrices are presented. To reduce decoding complexity, separating parity-check matrices with small number of rows are preferred. The minimum number of rows in a parity-check matrix separating a given maximum number of erasures is called the separating redundancy. Upper and lower bounds on the separating redundancies are derived. In particular, it is shown that the separating redundancies tend to grow linearly with the number of rows in full-rank parity-check matrices of codes. The separating redundancies of some classes of codes are determined for some maximum numbers of erasures.

关键词： Error and erasure decoding linear block code parity-check matrix separating matrix separating redundancy

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Practical Methods for Wireless Network Coding With Multiple Unicast Transmissions

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IEEE TRANSACTIONS ON COMMUNICATIONS 2013年第3期61卷 1123-1133页

作者： Aktas, Tugcan Yilmaz, A. Ozgur Aktas, Emre Middle E Tech Univ Dept Elect & Elect Engn TR-06531 Ankara Turkey Hacettepe Univ Dept Elect & Elect Engn Ankara Turkey

We propose a simple yet effective wireless network coding and decoding technique for a multiple unicast network. It utilizes spatial diversity through cooperation between nodes which carry out distributed encoding operations dictated by generator matrices of linear block codes. In order to exemplify the technique, we make use of greedy codes over the binary field and show that the arbitrary diversity orders can be flexibly assigned to nodes. Furthermore, we present the optimal detection rule for the given model that accounts for intermediate node errors and suggest a low-complexity network decoder using the sum-product (SP) algorithm. The proposed SP detector exhibits near optimal performance. We also show asymptotic superiority of network coding over a method that utilizes the wireless channel in a repetitive manner without network coding (NC) and give related rate-diversity trade-off curves. Finally, we extend the given encoding method through selective encoding in order to obtain extra coding gains.

关键词： Wireless network coding cooperative communication linear block code sum-product decoding unequal error protection

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On the Error Performance Bound of Ordered Statistics Decoding of linear block codes

On the Error Performance Bound of Ordered Statistics Decodin...

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Ad-Hoc and Sensor Networks Symposium

作者： Pawan Dhakal Roberto Garello Shree Krishna Sharma Symeon Chatzinotas Bjorn Ottersten DET - det.polito.it Politecnico di Torino SnT - securityandtrust.lu University of Luxembourg

ISBN: (纸本)9781479966653

In this paper, a novel simplified statistical approach to evaluate the error performance bound of Ordered Statistics Decoding (OSD) of linear block codes (LBC) is investigated. First, we propose a novel statistic which depicts the number of errors contained in the ordered received noisy codeword. Then, simplified expressions for the probability mass function and cumulative distribution function are derived exploiting the implicit statistical independence property of the samples of the received noisy codeword before reordering. Second, we incorporate the properties of this new statistic to derive the simplified error performance bound of the OSD algorithm for all order-I reprocessing. Finally, with the proposed approach, we obtain computationally simpler error performance bounds of the OSD than those proposed in literature for all length LBCs.

关键词： error performance Optical Scanning Device linear block code mass function Bound Ordered DECODING Cumulative distribution function codeword

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Matrix theory for minimal trellises

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DESIGNS codeS AND CRYPTOGRAPHY 2019年第11期87卷 2507-2536页

作者： Duursma, Iwan M. Univ Illinois Dept Math Urbana IL 61801 USA Univ Illinois Coordinated Sci Lab Urbana IL 61801 USA

Trellises provide a graphical representation for the row space of a matrix. The product construction of Kschischang and Sorokine builds minimal conventional trellises from matrices in minimal span form. Koetter and Vardy showed that minimal tail-biting trellises can be obtained by applying the product construction to submatrices of a characteristic matrix. We introduce the unique reduced minimal span form of a matrix and we obtain an expression for the unique reduced characteristic matrix. Among new properties of characteristic matrices we prove that characteristic matrices are in duality if and only if they have orthogonal column spaces, and that the transpose of a characteristic matrix is again a characteristic matrix if and only if the characteristic matrix is reduced. These properties have clear interpretations for the unwrapped unit memory convolutional code of a tail-biting trellis, they explain the duality for the class of Koetter and Vardy trellises, and they give a natural relation between the characteristic matrix based Koetter-Vardy construction and the displacement matrix based Nori-Shankar construction. For a pair of reduced characteristic matrices in duality, one is lexicographically first in a forward direction and the other is lexicographically first in the reverse direction. This confirms a conjecture by Koetter and Vardy after taking into account the different directions for the lexicographical ordering.

关键词： linear block code Minimal trellis Tail-biting trellis Characteristic generator Koetter and Vardy conjecture

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A new OFDM-CDMA uplink concept with M-ary orthogonal modulation

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EUROPEAN TRANSACTIONS ON TELECOMMUNICATIONS 1999年第4期10卷 377-389页

作者： Dekorsy, A Kammeyer, KD Univ Bremen Dept Telecommun FB 1 D-28334 Bremen Germany

This paper proposes the application of M-ary orthogonal Walsh modulation for an OFDM-CDMA uplink transmission. Beside the examination of general system properties, it is shown that decision-directed phase estimation represents a channel estimation concept suitable for the new system. The Walsh modulation can also be interpreted as a linear block code with low decoding complexity, and the paper concerns the serial concatenation of convolutional codes (CC) with Walsh modulation. New aspects arise since the CC mainly operates in time domain, and the Walsh modulation is merely arranged in frequency domain. In this context, we derive the bit specific reliability information for maximum likelihood (ML) soft decoding of the CC and discuss the trade-off between coding and spreading in case of sufficient and non-sufficient frequency interleaving. Throughout the discussions, the results are always compared with BPSK modulation performance, and it can clearly be demonstrated that M-ary Walsh modulation significantly outperforms BPSK modulation in all aspects considered in this work. Although the specific simulations are related to the European Hiperlan/2 standardization, the results are valid in general.

关键词： up link Orthogonal Valid Binary phase shift keying TIME-DOMAIN linear block code Phase estimation block codes Frequency-domain analysis

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Identification codes: A Topical Review With Design Guidelines for Practical Systems

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IEEE ACCESS 2023年 11卷 14961-14982页

作者： Von Lengerke, Caspar Hefele, Alexander Cabrera, Juan A. A. Kosut, Oliver Reisslein, Martin Fitzek, Frank H. P. Tech Univ Dresden Deutsch Telekom Chair Commun Networks D-01062 Dresden Germany Arizona State Univ Sch ECEE Tempe AZ 85287 USA Tech Univ Dresden Ctr Tactile Internet Human In The Loop CeTI D-01062 Dresden Germany

A wide range of information technology applications require the identification of a particular message or label that represents the identity of an object at a distance, e.g., over a wireless channel. Conventionally, the underlying information that represents the identity is transmitted over the channel, following the information-theoretic concept of message transmission. If the purpose of the interaction over the channel is only to verify (match) an identity, then the concept of identification over channels-utilizing the identification codes that have been developed by the information theory community-can provide an exponential efficiency gain over message transmission. This topical review article conducts for the first time a comprehensive detailed evaluation of the existing identification codes for the practically relevant regime of finite parameters. We examine essentially all published identification codes, including codes based on inner constant weight codes that are concatenated with outer linear block codes, such as Reed-Solomon and Reed-Muller codes. Specifically, we conduct a holistic identification code comparison based on the logarithm of the number of representable identities (in shannon), the size (in bit) of the transmitted cue that represents an identity, and the corresponding type II error probability bound for essentially all existing identification codes. Based on the resulting insights, we formulate guidelines for the design of practical (finite-parameter) identification codes. For instance, we find that a linear block code (without concatenation with a sophisticated inner constant-weight code) is sufficient for most practical identification code usages.

关键词： codes block codes Error probability Symbols Wireless communication Reed-Solomon codes Object recognition Beyond-Shannon communication error probability false-positive identification goal-oriented communication linear block code identity verification performance metrics

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A Revisit to Ordered Statistics Decoding: Distance Distribution and Decoding Rules

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IEEE TRANSACTIONS ON INFORMATION THEORY 2021年第7期67卷 4288-4337页

作者： Yue, Chentao Shirvanimoghaddam, Mahyar Vucetic, Branka Li, Yonghui Univ Sydney Sch Elect & Informat Engn Sydney NSW 2006 Australia

This paper revisits the ordered statistics decoding (OSD). It provides a comprehensive analysis of the OSD algorithm by characterizing the statistical properties, evolution and the distribution of the Hamming distance and weighted Hamming distance from codeword estimates to the received sequence in the reprocessing stages of the OSD algorithm. We prove that the Hamming distance and weighted Hamming distance distributions can be characterized as mixture models capturing the decoding error probability and code weight enumerator. Simulation and numerical results show that our proposed statistical approaches can accurately describe the distance distributions. Based on these distributions and with the aim to reduce the decoding complexity, several techniques, including stopping rules and discarding rules, are proposed, and their decoding error performance and complexity are accordingly analyzed. Simulation results for decoding various eBCH codes demonstrate that the proposed techniques can significantly reduce the decoding complexity with a negligible loss in the decoding error performance.

关键词： Hamming distance Complexity theory Iterative decoding Maximum likelihood decoding Ultra reliable low latency communication Error probability Degradation Gaussian mixture Hamming distance linear block code ordered statistics decoding soft decoding

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