Huseyin Balli, Xijin Yan, Zhen Zhang · 2007
In this paper, we study the error correction capability of random linear network error correction codes (Z. Zhang, 2006). We derive bounds on the probability mass function of the minimum distance of a random network error correction code and the field size required for the existence of a network error correction code with a given degradation, which is the difference between the highest possible minimum distance in the Singleton bound and the minimum distance of the code. The main tool that we use to study these problems is an improved bound on the failure probability of random linear network codes that at one or more sinks, the source messages are not decodable. This problem was originally studied in T. Ho et al. (2006).
Cited by 22
Hal Id Hal · 2015
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Cited by 0
Toshinori Deguchi, Keisuke Matsuno, Toshiki Kimura et al. · 2009
Neural networks are able to learn more patterns with the incremental learning than with the correlative learning. The incremental learning is a method to compose an associative memory using a chaotic neural network. In the former work, it was found that the capacity of the network increases along with its size, with some threshold value and that it decreases over that size. The threshold value and the capacity varied by the learning parameter. In this paper, the capacity of the networks was investigated by changing the learning parameter. Through the computer simulations, it turned out that the capacity increases in proportion to the network size. Then, the error correction capability is estimated with learned patterns changing to the maximum capacity.
Cited by 4
Stéphanie Dib, François Rodier · Contemporary mathematics - American Mathematical Society · 2017
We present an asymptotic limit between correctable and uncorrectable errors on the Reed-Muller codes of any order and give its value. This limit is theoretical and does not depend on any decoding algorithm.
Cited by 0Open access
Marco Annaratone, R. Stefanelli · 1983
This paper presents a technique for increasing the reliability of arithmetic units. An error model is then presented; this model we'll represents the faulty behavior of many arithmetic units. The Residue Number System and its related properties are used in order to obtain a simple architecture (called Reliability Network, R-Net). The main characteristics of the presented technique are a significant reduction in the number of gales and a limited increase of global execution times. The extensive use of combinational logic makes it possible to implement the R-Net almost completely by means of Programmable Logic Arrays (PLA's). Finally, both the intrinsic regularity of the R-Net and its simple internal interconnection scheme make this approach suitable for a practical VLSI implementation.
Cited by 17
T. Helleseth, T. Klove, V.I. Levenshtein · 2003
In this paper, the error-correction capability of binary linear codes and the discrete simplex problem is discussed.
Cited by 1
Ingleâ ü, Ashok D., Siewiorek, Daniel P. · Research Showcase @ Carnegie Mellon University (Carnegie Mellon University) · 1973
Cited by 0
Ingle╠ü, Ashok D., Siewiorek, Daniel P. · Figshare · 2018
Computer Science Department
Cited by 0Open access
Ingle╠ü, Ashok D., Siewiorek, Daniel P. · KiltHub Repository · 2018
Computer Science Department
Cited by 0Open access
P.K. Lala, B. Kiran Kumar · 2003
The use of very deep submicron technology makes VLSI-based digital systems more susceptible to transient or soft errors, and thus compromises their reliability. This paper proposes an FPGA architecture inspired by the human immune system that allows tolerance of transient errors. The architecture is composed of a two-dimensional array of identical functional cells with different genetic codes. These codes are chosen based on the required functions to be performed by the functional cells. An error in a FPGA based digital system designed using the proposed architecture is treated as an antigen by the system. Using its distributed defense mechanism the system heals itself from the effect of the error. A major advantage of this architecture is that, the outputs of functional cells are connected to the inputs of other physically adjacent functional cells without having to go through complicated routing. Thus, lengthy communication paths between cells are avoided.
Cited by 1
Dongyuan Liu (6504), Chouxian Ma (391731), Weiguo Hong (391728) et al. · Figshare · 2015
Cited by 0Open access
Shashi Kiran Chilappagari, Bane Vasic · IEEE Transactions on Information Theory · 2009
In this paper, the error-correction capability of column-weight-three low-density parity-check (LDPC) codes when decoded using the Gallager A algorithm is investigated. It is proved that a necessary condition for a code to correct all error patterns with up to k ges 5 errors is to avoid cycles of length up to 2k in its Tanner graph. As a consequence of this result, it is shown that given any alpha > 0, exist N such that forall n > N, no code in the ensemble of column-weight-three codes can correct all alphan or fewer errors. The results are extended to the bit flipping algorithms.
Cited by 36Open access
Bane Vasic, et al. · 2007
In this paper, we investigate the error correction capability of column-weight-three LDPC codes when decoded using the Gallager A algorithm. We prove that the necessary condition for a code to correct k ≥ 5 errors is to avoid cycles of length up to 2k in its Tanner graph. As a consequence of this result, we show that given any α> 0, ∃N such that ∀n> N, no code in the ensemble of column-weight-three codes can correct all αn or fewer errors. We extend these results to the bit flipping algorithm.
Cited by 37
Shashi Kiran Chilappagari, Bane Vasić · ArXiv.org · 2007
In this paper, we investigate the error correction capability of column-weight-three LDPC codes when decoded using the Gallager A algorithm. We prove that the necessary condition for a code to correct $k \geq 5$ errors is to avoid cycles of length up to $2k$ in its Tanner graph. As a consequence of this result, we show that given any $α>0, \exists N $ such that $\forall n>N$, no code in the ensemble of column-weight-three codes can correct all $αn$ or fewer errors. We extend these results to the bit flipping algorithm.
Cited by 2Open access
Marcus Greferath, Cornelia Rößing · IFAC-PapersOnLine · 2022
Based on a recently presented approach to non-adaptive group testing in terms of residuated pairs on Boolean lattices, we extend our investigation into group testing to the noisy case. In this context, several concepts and techniques from traditional Coding Theory over finite fields need to be adapted and refined. We will touch a variety of relevant notions and concepts and provide some first sporadic examples of error-correcting group testing schemes. The possible applications are diverse and reach from simple search of defective items in production chains to mass testing under pandemic conditions.
Cited by 0Open access
M. N. Isaeva, A. A. Ovchinnikov · Scientific and technical journal of information technologies mechanics and optics · 2024
The most important method of ensuring data integrity is correcting errors that occur during information storage, processing or transmission. The error-correcting coding methods are used to correct errors. In real systems, noise processes are correlated. However, traditional coding and decoding methods use decorrelation, and it is known that this procedure reduces the maximum achievable characteristics of coding. Thus, constructing computationally efficient decoding methods that would correct grouped errors for a wide class of codes is an actual problem. In this paper the decoding by information sets is used to correct single bursts. This method has exponential complexity when correcting independent errors. The proposed approach uses a number of information sets linearly growing with code length, which provides polynomial decoding complexity. A further reduction of the number of information sets is possible with the proposed method of using dense information sets. It allows evaluating both the set of errors potentially corrected by the code and the characteristics of the decoder. An improvement of the decoding method using an error vector counter is proposed, which allows in some cases to increase the number of corrected error vectors. This method allows significantly reducing the number of information sets or increasing the number of corrected error vectors according to the minimum burst length criterion. The proposed decoders allow correction of single error bursts in polynomial time for arbitrary linear codes. The results of experiments based on standard array show that decoders not only correct all errors within the burst correcting capability of the code, but also a significant number of error vectors beyond of it. Possible directions of further research are the analysis of the proposed decoding algorithms for long codes where the method of analysis based on the standard array is not applicable; the development and analysis of decoding methods for multiple bursts and the joint correction of grouped and random errors.
Cited by 2Open access
Iosr Journals, M. K. Sandhya, S.Deepa · Figshare · 2014
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Amit M. Joshi, Samar Ansari, M. Ravikumar · 2017
The expansion in technology has explored the cost effective ways of replication & distribution for digital content with least effort. The digital watermark is a technique which can be useful to have an effective protection for authentication and proof of ownership. The proposed method uses Integer DCT with an error correction concept to improve the robustness of the watermarking system. The performance of proposed algorithm is validated on MATLAB in terms of Cross-Correlation with and without error correction code. The reliability of algorithm is also increased almost 10% to 20% with the help of error correction code. The payload of the proposed system is also higher compare to previous work. Experimental results have demonstrated the effectiveness against various attacks such as JPEG lossy compression, noise attacks and geometrical attacks. VLSI architecture of proposed algorithm is designed and hardware implementation is achieved to verify the real-time performance.
Cited by 1
Yu Han, Bin Fan, Chaoqiang Li et al. · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2016
The surface error correction ability is one of the important indicators to measure the performance of the active support system. In this paper, the correction force algorithm for the active support system of 1.2m thin meniscus mirror is introduced. Based on this algorithm, a simulation analysis is made. The simulation results show that the 1.2m active support system has excellent correction ability for Zernike polynomials term 4, 5, 6, 10 and 11, and has a good effect on the Zernike polynomials term 7 and 8.
Cited by 1
Iosr Journals, S. Sandhya · Figshare · 2014
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