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The Sufficient and Necessary Conditions for the Minimum Distance of the bch code C(q,q+1,3,h) to Be 3 and 4

IEEE TRANSACTIONS ON INFORMATION THEORY 2025年第6期71卷 4206-4213页

作者： Xu, Haojie Wu, Xia Lu, Wei Cao, Xiwang Southeast Univ Sch Math Nanjing 210096 Peoples R China Nanjing Univ Aeronaut & Astronaut Dept Math Nanjing 211100 Peoples R China

In this paper, the sufficient and necessary conditions for the minimum distance of the bch code C-(q,C-q+1,C-3,C-h) to be 3 and 4 are provided, respectively. Let d be the minimum distance of the bch code C-(q,C-q+1,C-3,C-h). The following results are proved: 1) for any q, d=3 if and only if gcd (2h+1,q+1) > 1;2) for q odd, d=4 if and only if gcd (2h+1,q+1)=1. By combining these conditions with the dimensions of these codes, the parameters of this bch code are determined completely when q is odd. Moreover, several infinite families of almost maximum distance separable (almost MDS or AMDS for short) codes are derived. Furthermore, a sufficient condition for these almost MDS codes to be distance-optimal and dimension-optimal locally repairable codes is presented. Based on these conditions, several examples are also given.

关键词： codes Linear codes codecs Polynomials Generators Vectors Symbols Sufficient conditions Memory Maintenance engineering Cyclic code bch code almost MDS code near MDS code locally repairable code

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Blind Reconstruction of Binary Primitive bch code Based on Error codeword Correction

Blind Reconstruction of Binary Primitive BCH Code Based on E...

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International Conference on Ubiquitous Communication (Ucom)

作者： Mu, Haochen Wu, Yunzhi Li, Li Southwest Jiaotong Univ Sch Informat Sci & Technol Chengdu Peoples R China

ISBN: (纸本)9798350374223;9798350374216

In this paper, a blind reconstruction method of binary primitive bch code is proposed, which can identify the generator polynomial of bch code from received noisy bitstreams. Firstly, error codewords are exposed according to the fact that correct codeword polynomials shall have consecutive roots. Secondly, the recovery of error codewords will be fast completed by leveraging the parity-check matrix of bch code. Then, the consecutive roots of bch code are determined by measuring the discrepancy between their experimental occurring probability and their theoretical occurring probability. Finally, the generator polynomial of bch code are reconstructed based on the detected roots. Simulation results show that for the bch codes whose error correction capability exceed 2 bits, the proposed method outperforms the reconstruction method using single-error correction.

关键词： bch code blind reconstruction error codeword correction

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High Detection Rate bch code with CRC code for Memory Application 19

High Detection Rate BCH Code with CRC Code for Memory Applic...

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19th International SoC Design Conference (ISOCC) - SoC Technology Towards a New Era of Innovation

作者： Kim, Minseo Park, Jongsun Korea Univ Dept Elect Engn Seoul South Korea

ISBN: (纸本)9781665459716

With the aggressive scaling of DRAM process technology, the reliability degradation has become a critical issue, which inevitably increases the demand for more powerful error correction code (ECC) than conventional Hamming code. Although double error correction (DEC) bch code needs less parity bits than other DEC codes, it cannot detect the errors larger than 3 bits. In this paper, we present a novel bch code combined with cyclic redundancy check (CRC) code which can effectively detect multi-bit errors. By employing the CRC code, the proposed bch code corrects double errors with a 3-bit error detection probability of 84%. In addition, by reusing the bch encoder as CRC encoder and decoder in the proposed bch, the area overhead of the proposed bch is only 7.8% compared to the conventional bch code.

关键词： Error Correction code bch code

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Fast Blind Recognition of bch code Based on Spectral Analysis and Probability Statistics

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IEEE COMMUNICATIONS LETTERS 2021年第10期25卷 3170-3174页

作者： Chang, Yanyan Zhang, Wei Wang, Hao Liu, Yanyan Tianjin Univ Sch Microelect Tianjin 300072 Peoples R China Nankai Univ Coll Elect Informat & Opt Engn Tianjin 300071 Peoples R China

This letter presents a fast blind recognition method for Bose, Chaudhuri, and Hocquenghem (bch) code from noisy intercepted bit-streams. This approach employs the fact that the t-error-correcting bch code has 2t continuous roots, and the roots correspond with the zero spectral. Specifically, the Galois field Fourier transform is simplified (S-GFFT) by using the property of conjugate roots. Then, the distribution characteristics of continuous zero spectra are analyzed. If the continuous zero spectra satisfy the threshold condition which is derived by the probability of zero spectrum component, the corresponding estimated length is the code length, and the relevant positions correspond to the continuous roots of the generated polynomial. Finally, the generator polynomial can be reconstructed based on algebras theory. Compared to the existing solutions, the computational amount of S-GFFT at most accounts for 60% of GFFT, and the proposed scheme manages to recognize the code parameters without traversing the whole candidate datasets.

关键词： Generators Probability Encoding Spectral analysis Fourier transforms Noise measurement Decoding Fast blind recognition bch code Galois field Fourier transform the~probability of zero spectrum component

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On components of the Kerdock codes and the dual of the bch code C1,3

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DISCRETE MATHEMATICS 2020年第2期343卷

作者： Mogilnykh, I. Yu. Solov'eva, F. I. Sobolev Inst Math Novosibirsk Russia Novosibirsk State Univ Novosibirsk Russia

In the paper we investigate the structure of i-components of two classes of codes: the Kerdock codes and the duals of the linear uniformly packed codes with parameters of the primitive double-error-correcting bch code. We prove that for any admissible length the punctured Kerdock code consists of two i-components and the duals of the linear uniformly packed codes with parameters of the primitive double-error-correcting bch code is an i-component for any i. We give an alternative proof for the fact presented by De Caen and van Dam in 1999 that the restrictions of the Hamming scheme to the doubly shortened Kerdock codes are association schemes. (C) 2019 Published by Elsevier B.V.

关键词： Kerdock code bch code Uniformly packed code Association scheme i-component t-design

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Asymptotically Good codes Obtained by an Extended Primitive bch code Concatenated with Interleaved codes 8

Asymptotically Good Codes Obtained by an Extended Primitive ...

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IEEE 8th Joint International Information Technology and Artificial Intelligence Conference (ITAIC)

作者： Cheng, Feng Southwest Jiaotong Univ Sch Math Chengdu 610031 Sichuan Peoples R China

How to construct asymptotically good codes is one of the hottest topic in modern coding theory. In this paper, we concatenated an extended primitive bch outer code with a class of binary inner codes constructed by an ... 详细信息

ISBN: (纸本)9781538681787

关键词： Asymptotically good codes Asymptotically good code classes bch code Interleaved code Gilbert-Varshamov bound Weight spectra

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Performance Analysis Method for IEEE 802.15.6 Based WBANs with Adaptive bch code Rates

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WIRELESS PERSONAL COMMUNICATIONS 2017年第3期94卷 605-619页

作者： Do Thanh Quan Pham Thanh Hiep Kohno, Ryuji Yokohama Natl Univ Yokohama Kanagawa Japan Yokohama Natl Univ Div Elect & Comp Engn Yokohama Kanagawa Japan Le Quy Don Tech Univ Hanoi Vietnam

The IEEE 802.15.6 was established in Feb 2012 due to emergency of wireless body area networks (WBANs). In order to improve the performance of WBANs, the physical (PHY) layer, medium access control (MAC) layer and network layer have been discussed in a number of literatures. Although there are also many previous works on performance analysis for WBANs, a noise free was frequently assumed when contention error is taken into account in MAC layer. It means that in these works bit error rates (BERs) were not taken into consideration adequately. In this paper, we propose the Markov chain Monte Carlo (MCMC) method to analyze performance in the PHY and MAC layers for WBANs, in which BERs are taken into consideration. The BERs are theoretically analyzed depending on different Bose-Chaudhuri-Hocquenghem (bch) code rates, and then the bch code rate for every sensor node is optimized in sense of the highest throughput while assuming the signal to noise ratio (SNR) of every sensor node is different. Furthermore, the dependence of throughput on the BER is clearly explained by calculating the access probability for every sensor node in large SNR region. The bch code was adopted as an example and then adaptive bch code rates for WBANs were proposed. The application of proposal method to other error correcting codes is straightforward.

关键词： Wireless body area networks Discrete time Markov chain method bch code Bit error rate IEEE 802.15.6

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Multilevel Adaptive Wavelet bch code Method for Copyright Protection in Audio Watermarking System 4

Multilevel Adaptive Wavelet BCH Code Method for Copyright Pr...

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IEEE Asia Pacific Conference on Wireless and Mobile (APWiMob)

作者： Safitri, Irma Ginanjar, Rizki R. Univ Telkom Sch Elect Engn Bandung Indonesia

ISBN: (纸本)9781538623732

Audio watermarking is used as a tool to avoid the illegal manipulation of audio products. In this research, we proposed the audio watermarking system with adaptive bch code multilevel wavelet method. We use three types of bch codes: 15,11,1;15,7,2;and 15,5,3. Our work show that the perceptual quality, robustness and watermark security are varies to the type of bch codes. At quantization spacing of 0.1, ODG values can reach-0.7 for bch code 15,11,1 and-1 for bch code 15,5,3 in the LPF attack. Meanwhile SNR values can reach 32.7 dB for bch code 15,11,1 and 29.8 dB for bch 15,5,3 in the LPF attack. The last, BER value of bch code 15,5,3 can reach zero as fastest as in 0.01 quantization spacing when our audio watermarking system is attacked by noise.

关键词： Audio Watermarking bch code DWT SVD

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Adaptive Multilevel Wavelet bch code Method in the Audio Watermarking System 3

Adaptive Multilevel Wavelet BCH Code Method in the Audio Wat...

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International Conference on Control, Electronics, Renewable Energy and Communications (ICCREC)

作者： Safitri, Irma Ginanjar, Rizki Rivai Rizal, Achmad Azizah Telkom Univ Sch Elect Engn Bandung Indonesia

ISBN: (纸本)9781538616673

In this research, we proposed the audio watermarking system with adaptive multilevel DWT (discrete wavelet transform) - SVD (singular value decomposition) based on bch (Bose-Chaudhuri-Hocquenghem) code. The host audio signal is embedded with a watermark signal in the form of an image signal accompanied by several attacks on the watermarking system. The results showed that the perceptual quality of audio in the form of ODG (Objective Difference Grade) and SNR (Signal to Noise Ratio) parameters for DWT (Discrete Wavelet Transormation) level 1 was higher than level 3. It can reach ODG level 1 = -0.68 and level 3 = -1.54 on LSC attack type;SNR level 1 = 31 dB and level 3 = 27 dB on LPF attack type. While for watermark image BER parameter, the result of the research shows that BER level 1 is worse than level 3, which can reach BER level 1 = 0.35 and level 3 = 0 on LPF attack. Higher decomposition level of wavelet makes the audio host file is less imperceptible to the attack, but higher robustness.

关键词： Audio Watermarking bch code DWT SVD

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Fast Decoder of bch code with Cyclic Decoding Method

Fast Decoder of BCH Code with Cyclic Decoding Method

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International Siberian Conference on Control and Communications (SIBCON)

作者： Mytsko, E. Malchukov, A. Novogilov, I. Kim, V. FSAEI HE NR Tomsk Polytech Univ Dept Comp Engn Tomsk Russia

Fast decoder of bch code (31, 16, 7) which based on matrix algorithm of syndromes computation and parallel data processing was developed. Functional blocks of developed device based on block- based design were describ... 详细信息

ISBN: (纸本)9781467383837

关键词： bch code codec fast decoder cyclic method error-correcting code block-based design

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