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Linear Network Error Correction Codes in Packet Networks 总被引:4,自引:0,他引:4
Zhen Zhang 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2008,54(1):209-218
In this paper, we study basic properties of linear network error correction codes, their construction and error correction capability for various kinds of errors. Our discussion is restricted to the single-source multicast case. We define the minimum distance of a network error correction code. This plays the same role as it does in classical coding theory. We construct codes that can correct errors up to the full error correction capability specified by Singleton bound for network error correction codes recently established by Cai and Yeung. We propose a decoding principle for network error correction codes, based on which we introduce two decoding algorithms and analyze their performance. We formulate the global kernel error correction problem and characterize the error correction capability of codes for this kind of error. 相似文献
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介绍了一种有效的字节式单向错误纠错码及其编码和译码算法。从对校验位数下限值的讨论可以看出,这里介绍的码优于字节式对称错误纠错码,并且近似最优。本文还介绍了字节式非对称错误纠错码。 相似文献
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On the Probability of Undetected Error for Linear Block Codes 总被引:1,自引:0,他引:1
The problem of computing the probability of undetected error is considered for linear block codes used for error detection. The recent literature is first reviewed and several results are extended. It is pointed out that an exact calculation can be based on either the weight distribution of a code or its dual. Using the dual code formulation, the probability of undetected error for the ensemble of all nonbinary linear block codes is derived as well as a theorem that shows why the probability of undetected error may not be a monotonic function of channel error rate for some poor codes. Several bounds on the undetected error probability are then presented. We conclude with detailed examples of binary and nonbinary codes for which exact results can be obtained. An efficient technique for measuring an unknown weight distribution is suggested and exact results are compared with experimental results. 相似文献
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数字通信系统通常采用前向纠错编码提高系统可靠性,传统干扰方法针对采用前向纠错编码通信系统的干扰效果较差,为了克服此缺点,提出了通过控制错误分布的脉冲干扰方法。分析了典型卷积码和RS码的纠错能力,根据2种纠错编码的特性分别探讨了干扰信号设计原则和方法。计算机仿真表明,针对不同的编码样式采用特定脉冲干扰参数,能够取得更好的干扰效果。 相似文献
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《IEEE transactions on information theory / Professional Technical Group on Information Theory》2009,55(12):5479-5490
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Burshtein D. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2008,54(2):517-530
The iterative bit flipping algorithm is applied to the standard regular low-density parity-check (LDPC) code ensemble. In the past, it was shown, for a typical code in the ensemble with left degree at least five and block length sufficiently large, that this algorithm can correct a linear (in the block length) number of worst case errors. In this paper, this result is extended to the case where the left degree is at least four. For the case where the left degree is larger than four, an improvement, compared to existing results, of several orders of magnitude is obtained on the fraction of worst case errors that can be corrected. It is also shown how the results can be further improved when random errors produced by the channel (as opposed to worst case errors) are considered. 相似文献
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介绍了神经网络与线性分组码之间的关系,并在文献[1]的基础上证明了软判决译码与求解能量函数最大值之间的等价性,然后以(7,4,3)汉明码为例介绍了神经网络在循环码硬判决、软判决译码中的应用。 相似文献
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定义了一类新的线性码,它具有结构简单、码率较大的特点。利用一般方法产生了纠多个错的线性码。计算出这类线性码的重量分布,关于码的自同构群也得到了一些结果。 相似文献
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网络编码对网络中的传输错误或恶意攻击十分敏感,如果网络拓扑和网络码对于网络的收点和发点都是已知的,这种类型的网络称为Coherent网络。在Coherent网络中,网络汉明重量的概念拉近了网络纠错码和传统纠错码之间的距离,传统纠错码的一些理论和方法有望在将来应用于网络纠错码。类似于传统纠错码,极小距离反映了网络纠错码的纠错能力。利用陪集码理论去描述和研究网络纠错码是一个令人感兴趣的研究方向。 相似文献
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This paper studies the implementation of Double Error Correction Orthogonal Latin Squares (OLS) in Xilinx Field Programmable Gate Arrays (FPGAs). Several existing options to implement the decoder are considered and evaluated. The results show that the decoder complexity can be significantly optimized by appropriately selecting the implementation that is better suited to the internal FPGA structure. A new implementation tailored for the FPGA structure is proposed, which has a more efficient physical resource utilization compared with the existing ones. It is shown that the improvement on resource utilization is also highly correlated with the soft error vulnerability. The proposed decoder scheme has a reduced soft error cross section compared with other implementations. Based on these results, it seems that optimizing the ECC implementation for FPGAs can be effective and may be useful for other codes. 相似文献
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Kashyap N. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2009,55(8):3501-3519
A tree decomposition of the coordinates of a code is a mapping from the coordinate set to the set of vertices of a tree. A tree decomposition can be extended to a tree realization, i.e., a cycle-free realization of the code on the underlying tree, by specifying a state space at each edge of the tree, and a local constraint code at each vertex of the tree. The constraint complexity of a tree realization is the maximum dimension of any of its local constraint codes. A measure of the complexity of maximum-likelihood (ML) decoding for a code is its treewidth, which is the least constraint complexity of any of its tree realizations.It is known that among all tree realizations of a linear code that extends a given tree decomposition, there exists a unique minimal realization that minimizes the state-space dimension at each vertex of the underlying tree. In this paper, we give two new constructions of these minimal realizations. As a by-product of the first construction, a generalization of the state-merging procedure for trellis realizations, we obtain the fact that the minimal tree realization also minimizes the local constraint code dimension at each vertex of the underlying tree. The second construction relies on certain code decomposition techniques that we develop. We further observe that the treewidth of a code is related to a measure of graph complexity, also called treewidth. We exploit this connection to resolve a conjecture of Forney's regarding the gap between the minimum trellis constraint complexity and the treewidth of a code. We present a family of codes for which this gap can be arbitrarily large. 相似文献
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随着高速多媒体业务的迅速发展,如何提高第三代移动通信系统(3G)以及新一代移动通信系统(Beyond3G)的性能和容量愈发受到人们的重视。在业务无线接入时的服务质量(QoS)问题上,高效的纠错编码是必不可少且行之有效的解决方法之一。文中简要回顾了纠错码在前两代移动通信中的应用,并着重介绍了目前的研究热点——Turbo码和LDPC码的研究现状及发展前景。 相似文献
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In this paper we propose memory protection architectures based on nonlinear single-error-correcting, double-error-detecting
(SEC-DED) codes. Linear SEC-DED codes widely used for design of reliable memories cannot detect and can miscorrect lots of
errors with large Hamming weights. This may be a serious disadvantage for many modern technologies when error distributions
are hard to estimate and multi-bit errors are highly probable. The proposed protection architectures have fewer undetectable
errors and fewer errors that are miscorrected by all codewords than architectures based on linear codes with the same dimension
at the cost of a small increase in the latency penalty, the area overhead and the power consumption. The nonlinear SEC-DED
codes are generalized from the existing perfect nonlinear codes (Vasil’ev codes, Probl Kibern 8:375–378, 1962; Phelps codes, SIAM J Algebr Discrete Methods 4:398–403, 1983; and the codes based on one switching constructions, Etzion and Vardy, IEEE Trans Inf Theory 40:754–763, 1994). We present the error correcting algorithms, investigate and compare the error detection and correction capabilities of
the proposed nonlinear SEC-DED codes to linear extended Hamming codes and show that replacing linear extended Hamming codes
by the proposed nonlinear SEC-DED codes results in a drastic improvement in the reliability of the memory systems in the case
of repeating errors or high multi-bit error rate. The proposed approach can be applied to RAM, ROM, FLASH and disk memories. 相似文献
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本文利用一类准循环码的结构进行计算机搜索,再加上通常的码的变换,共得到了七个新的二元线性码,它们都改进了文「1」中二元线性码极小距离的下界,其中有三个是最优的。 相似文献
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本文详细研究了线性不等保护能力码的码长上界,得到了一些优于文献[1]的结果,本文还讨论了新上界在线性不等保护能力码构造上的应用。 相似文献