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golay code modulation in low-power laser-ultrasound

ULTRASONICS 2013年第1期53卷 122-129页

作者： Veres, Istvan A. Cleary, Alison Thursby, Graham Mckee, Campbell Armstrong, Ian Pierce, Gareth Culshaw, Brian Res Ctr Nondestruct Testing GmbH A-4040 Linz Austria Univ Strathclyde Dept Elect & Elect Engn Ctr Microsyst & Photon Glasgow G1 1XW Lanark Scotland Univ Strathclyde Dept Elect & Elect Engn Ctr Ultrason Engn Glasgow G1 1XW Lanark Scotland

The current work presents a correlation-based detection technique with application in modulated laser-ultrasonics. In standard use of coded sequences the impulse response of a system is recovered in the time domain with improved signal to noise ratio (SNR). The presented method is an extension of this technique, where the response to a chirped waveform is restored with improved SNR;hence, the response is in a well-defined frequency range. To achieve this goal the chirped waveforms are modulated by golay codes. It will be shown that the response to this bandlimited carrier waveform can be recovered in the time domain with improved signal to noise ratio using a cross-correlation technique. Improvement in the SNR is discussed analytically and it is shown that this improvement is proportional to the square root of the length of the applied sequences. Experimental applications in laser-ultrasound are shown using modulated laser diodes as excitation sources with an output power of similar to 1 W. In the experiments a plate with a thickness of 50 mu m is investigated using Lamb waves in the MHz range to confirm the predicted improvement in the SNR. golay codes with three different lengths were used with 7, 9 and 11 bits resulting in 2(7) = 128, 2(9) = 512, and 2(11) = 2048 repetitions in an individual signal, respectively. The predicted improvements of 2 in the SNR between the 7 and 9 bits, and between the 9 and 11 bits waveforms, respectively, were well approximated by the experimentally obtained values of 1.83 and 2.17. As Lamb wave dispersion curves can be used for the characterization of plates or layered samples by inverse problems, it is also shown that by using multiple measurement points the recovered waveforms can be utilized in the evaluation of the dispersion relation. (C) 2012 Elsevier B.V. All rights reserved.

关键词： coded sequence golay code Modulation Lamb waves

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golay code Based Bit Mismatch Mitigation for Wireless Channel Impulse Response Based Secrecy Generation

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IEEE ACCESS 2019年 7卷 2999-3007页

作者： Shen, Chen Li, Hao Sahin, Gokhan Choi, Hyeong-Ah Shah, Ogendra George Washington Univ Dept Comp Sci Washington DC 20052 USA Miami Univ Dept Elect & Comp Engn Oxford OH 45056 USA

The wireless radio communications channel between two legitimate user terminals has long been considered as a renewable source of shared secrecy. As characterization of the channel, the time-varying channel impulse response (CIR) is commonly used for this purpose due to its reciprocity and inherent difficulty in being captured by an adversary. While each terminal generates a secret key at its side, based on its own channel measurements combined with an independent noise component, mismatches may occur in the extracted information or in the obtained bit sequences after a sampling and quantization process. To mitigate such bit mismatches, we propose a method that utilizes the properties of the golay code to correct or detect the bit mismatches for CIR-based secret key agreement. In our approach, the reconciliation information in the transmission is deliberately designed to hide the original shared information (perfect or imperfect). The correctness of our bit mismatch mitigation algorithm is thoroughly analyzed for all possible scenarios. In addition, the effectiveness of our algorithm is validated through simulations using MATLAB for generated CIR data, the results of which match our theoretical analysis. Our design is shown to be secure and optimal by security analysis and comparisons between our proposed algorithm and its variants. The comparisons with related techniques and the scenarios in which our design can benefit are also discussed.

关键词： Information reconciliation secrecy generation golay code

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Minimal tail-biting trellises: The golay code and more

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IEEE TRANSACTIONS ON INFORMATION THEORY 1999年第5期45卷 1435-1455页

作者： Calderbank, AR Forney, GD Vardy, A AT&T Shannon Labs Florham Pk NJ 07932 USA Motorola Inc Mansfield MA 02048 USA Univ Calif San Diego Dept Elect & Comp Engn La Jolla CA 92093 USA

Tail-biting trellis representations of block codes are investigated. We develop some elementary theory, and present several intriguing examples, which we hope will stimulate further developments in this field. In particular, we construct a 16-state 12-section structurally invariant tail-biting trellis for the (24, 12, 8) binary golay code. This tail-biting trellis representation is minimal: it simultaneously minimizes all conceivable measures of state complexity. Moreover, it compares favorably with the minimal conventional 12-section trellis for the golay code, which has 256 states at its midpoint, or with the best quasi-cyclic representation of this code, which leads to a 64-state tail-biting trellis, Unwrapping this tail-biting trellis produces a periodically time-varying 16-state rate-1/2 "convolutional golay code" with d = 8, which has attractive performance/complexity properties. We furthermore show that the (6, 3, 4) quaternary hexacode has a minimal 8-state group tail-biting trellis, even though it has no such linear trellis over F-4. Minimal tail-biting trellises are also constructed for the (8, 4, 4) binary Hamming code, the (4, 2, 3) ternary tetracode, the (4, 2, 3) code over F-4, and the Z(4)-linear (8, 4, 4) octacode.

关键词： convolutional codes golay code hexacode iterative decoding tail-biting trellises

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Reversible Biosignal Steganography Approach for Authenticating Biosignals Using Extended Binary golay code

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IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS 2021年第1期25卷 35-46页

作者： Rahman, Mohammad Saidur Khalil, Ibrahim Yi, Xun RMIT Univ Sch Sci Melbourne Vic 3000 Australia

We present a reversible biosignal steganography method to authenticate the source of biosignal in this paper. Cloud is being a popular platform for storing a large volume of biosignals such as an electrocardiogram (ECG), electroencephalogram (EEG), and photoplethysmogram (PPG). However, outsourcing biosignals to the cloud may introduce authenticity issues. For instance, patient data can be altered, or fake patient data can be inserted by the dishonest cloud service provider or attacker for giving benefits to business organizations such as insurance service providers. Steganography approaches can be used to hide data sources identification data before outsourcing to the cloud for maintaining authenticity. Existing biosignal steganography approaches fail to reconstruct original biosignal after applying a reverse data hiding technique. In other words, current biosignal steganography approaches are irreversible. Reversible biosignal steganography method is required for protecting biosignal data from deterioration and efficient use by its stakeholders. In this work, we develop a reversible biosignal steganography approach using the Extended Binary golay code based error correction method. Our proposed method embeds secret authentication message as an error within different types of biosignals such as ECG, PPG, and EEG. Extended Binary golay code based error correction method is used to extract the secret message, and reconstruct original biosignal. We conduct a set of experiments for evaluating the performance of our proposed method.

关键词： Bioinformatics Electrocardiography Error correction codes Medical services Electroencephalography Cloud computing Decoding Reversible biosignal steganography lossless biosignal steganography biosignal authenticity reversible data hiding golay code

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Fast decoding of the (23,12,7) golay code with four-error-correcting capability

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EUROPEAN TRANSACTIONS ON TELECOMMUNICATIONS 2011年第7期22卷 388-395页

作者： Chu, Shao-I Lee, Hung-Peng Chang, Hsin-Chiu Fortune Inst Technol Dept Comp Sci & Informat Engn Kaohsiung 83160 Taiwan I Shou Univ Dept Informat Engn Kaohsiung 84001 Taiwan

In this paper, a fast and efficient decoding algorithm for correcting the (23, 12, 7) golay code up to four errors is presented. The aim of this paper is to develop a fast syndrome-group search method for finding the candidate codewords by utilizing the property that the syndromes of the weight-4 error patterns are identical to that of the weight-3 error pattern. When the set of the candidate codewords is constructed, the most likely one is determined by assessing the corresponding correlation metrics. The well-known Chase-II decoder, which needs to perform the hard-decision decoder multiple times, acts as a comparison basis. Simulation results over the additive white Gaussian noise channel show that the decoding complexity of the proposed method is averagely reduced by at least 86% in terms of the decoding time. Furthermore, the successful decoding percentage of the new decoder in the case of four errors is always superior to Chase-II decoder. At the signal-to-noise ratio of 0?dB, the proposed algorithm still can correct up to 97.40% weight-4 error patterns. The overall bit error rate performance of the proposed decoder is close to that of Chase-II decoder. It implies that the new decoder is beneficial to the practical implementation. Copyright (c) 2011 John Wiley & Sons, Ltd.

关键词： soft decision decoding golay code error pattern syndrome error-correcting code syndrome-group search

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The sextuply shortened binary golay code is optimal

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DESIGNS codeS AND CRYPTOGRAPHY 2019年第2-3期87卷 341-347页

作者： Ostergard, Patric R. J. Aalto Univ Sch Elect Engn Dept Commun & Networking POB 15400 Aalto 00076 Finland

The maximum size of unrestricted binary three-error-correcting codes has been known up to the length of the binary golay code, with two exceptions. Specifically, denoting the maximum size of an unrestricted binary code of length n and minimum distance d by A(n,d), it has been known that 64A(18,8)68 and 128A(19,8)131. In the current computer-aided study, it is shown that A(18,8)=64 and A(19,8)=128, so an optimal code is obtained even after shortening the extended binary golay code six times.

关键词： Classification Clique Double counting Error-correcting code golay code

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EVEN MORE EFFICIENT BOUNDED-DISTANCE DECODING OF THE HEXAcode, THE golay code, AND THE LEECH LATTICE

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IEEE TRANSACTIONS ON INFORMATION THEORY 1995年第5期41卷 1495-1499页

作者： VARDY, A Coordinated Science Laboratory University of Illinois Urbana-Champaign Urbana IL USA

We present a new bounded-distance decoding algorithm for the hexacode, which requires at most 34 real operations in the worst case, as compared to 57 such operations in the best previously known decoder. The new algorithm, is then employed for bounded-distance decoding of the Leech lattice and the golay code. The error-correction radius of the resulting decoders is equal to that of a maximum-likelihood decoder. The resulting decoding complexity is at most 331 real operations for the Leech lattice and at most 121 operations for the golay code. For all the three codes-the hexacode, the golay code, and the Leech lattice-the proposed decoders are considerably more efficient than any decoder presently known.

关键词： LEECH LATTICE golay code HEXAcode BOUNDED-DISTANCE DECODING

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An Efficient Single and Double-Adjacent Error Correcting Parallel Decoder for the (24,12) Extended golay code

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IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS 2016年第4期24卷 1603-1606页

作者： Reviriego, Pedro Liu, Shanshan Xiao, Liyi Maestro, Juan Antonio Univ Antonio Nebrija Madrid 28040 Spain Harbin Inst Technol Microelect Ctr Harbin 150001 Peoples R China

Memories that operate in harsh environments, like for example space, suffer a significant number of errors. The error correction codes (ECCs) are routinely used to ensure that those errors do not cause data corruption. However, ECCs introduce overheads both in terms of memory bits and decoding time that limit speed. In particular, this is an issue for applications that require strong error correction capabilities. A number of recent works have proposed advanced ECCs, such as orthogonal Latin squares or difference set codes that can be decoded with relatively low delay. The price paid for the low decoding time is that in most cases, the codes are not optimal in terms of memory overhead and require more parity check bits. On the other hand, codes like the (24,12) golay code that minimize the number of parity check bits have a more complex decoding. A compromise solution has been recently explored for Bose-Chaudhuri-Hocquenghem codes. The idea is to implement a fast parallel decoder to correct the most common error patterns (single and double adjacent) and use a slower serial decoder for the rest of the patterns. In this brief, it is shown that the same scheme can be efficiently implemented for the (24,12) golay code. In this case, the properties of the golay code can be exploited to implement a parallel decoder that corrects single-and double-adjacent errors that is faster and simpler than a single-error correction decoder. The evaluation results using a 65-nm library show significant reductions in area, power, and delay compared with the traditional decoder that can correct single and double-adjacent errors. In addition, the proposed decoder is also able to correct some triple-adjacent errors, thus covering the most common error patterns.

关键词： Double adjacent error correction (DAEC) error correction codes (ECCs) golay code memory single error correction (SEC) triple-adjacent error correction

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ON MINIMAL DECODING SETS FOR THE EXTENDED BINARY golay code

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IEEE TRANSACTIONS ON INFORMATION THEORY 1992年第5期38卷 1560-1561页

作者： ANDERSON, JL Jacksonville FL 32211 7265 Oakwood Dr. United States

Minimal decoding sets consisting of fourteen permutations have been found for the (24,12,8) extended binary golay code. It is shown that by properly sequencing the permutations of one such set, the average number of p... 详细信息

关键词： PERMUTATION DECODING golay code MINIMAL DECODING SET

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Symbol-by-symbol APP decoding of the golay code and iterative decoding of concatenated golay codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 1999年第7期45卷 2558-2562页

作者： Li, P Yeung, KL City Univ Hong Kong Dept Elect Engn Hong Kong Peoples R China

An efficient coset based, symbol-by-symbol soft-in/soft-out APP decoding algorithm is presented for the golay code. Tts application in the iterative decoding of concatenated golay codes is examined.

关键词： concatenated codes coset decoding golay code iterative decoding turbo codes turbo decoding

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