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《IEEE transactions on information theory / Professional Technical Group on Information Theory》1978,24(2):205-212
Classes of codes for a multichannel communication system are considered. A fast algorithm is developed to calculate syndromes of multichannel linear systematic codes, including both block and convolutional codes, by using a direct sum of Galois fields. 相似文献
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For BCH codes with symbols from rings of residue class integers modulo m, denoted by Zm , we introduce the analogue of Blahut's frequency domain approach for codes over finite fields and show that the problem of decoding these codes is equivalent to the minimal shift register synthesis problem over Galois rings. A minimal shift register synthesis algorithm over Galois rings is obtained by straightforward extention of the Reeds-Sloane algorithm which is for shift register synthesis over Zm . 相似文献
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This paper presents the design of space–time block codes (STBCs) over maximum rank distance (MRD) codes, energy‐efficient STBCs, STBCs using interleaved‐MRD codes, the use of Gaussian integers for STBCs modulation, and Gabidulin's decoding algorithm for decoding STBCs. The design fundamentals of STBCs using MRD codes are firstly put forward for different number of transmit antennas. Extension finite fields (Galois fields) are used to design these linear block codes. Afterward, a comparative study of MRD‐based STBCs with corresponding orthogonal and quasi‐orthogonal codes is also included in the paper. The simulation results show that rank codes, for any number of transmit antennas, exhibit diversity gain at full rate contrary to orthogonal codes, which give diversity gain at full rate only for two transmit antennas case. Secondly, an energy‐efficient MRD‐STBC is proposed, which outperforms orthogonal STBC at least for 2 × 1 antenna system. Thirdly, interleaved‐MRD codes are used to construct higher‐order transmit antenna systems. Using interleaved‐MRD codes further reduces the complexity (compared with normal MRD codes) of the decoding algorithm. Fourthly, the use of Gaussian integers is utilized in mapping MRD‐based STBCs to complex constellations. Furthermore, it is described how an efficient and computationally less complex Gabidulin's decoding algorithm can be exploited for decoding complex MRD‐STBCs. The decoding results have been compared against hard‐decision maximum likelihood decoding. Under this decoding scheme, MRD‐STBCs have been shown to be potential candidate for higher transmit antenna systems as the decoding complexity of Gabidulin's algorithm is far less, and its performance for decoding MRD‐STBCs is somewhat reasonable. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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光通信中一种基于有限域循环子群的QC-LDPC码构造方法 总被引:1,自引:1,他引:0
基于有限域循环子群方法提出了一种结构简单,可以灵活选择码长、码率,并且编译码复杂度低的准循环低密度奇偶校验(QC-LDPC)码构造方法。利用此方法构造出适合光通信系统传输的规则QC-LDPC(5334,4955)码。仿真结果表明该码型利用和积迭代译码算法在加性高斯白噪声信道中取得了很好的性能,比已广泛应用于光通信中的经典RS(255,239)码具有更好的纠错性能。因此所构造的QC-LDPC(5334,4955)码能较好地适用于高速长距离光通信系统。 相似文献
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本文讨论了分组码的格图结构,给出了某些BCH码L段格图结构,并据此提出了BCH码的快速最大似然译码算法,同时讨论了qm元分组码的q元映象的译码问题,给出了q元映象的直和划分结构和相应的译码算法。 相似文献
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Jun Ma Vardy A. Zhongfeng Wang 《Very Large Scale Integration (VLSI) Systems, IEEE Transactions on》2007,15(11):1225-1238
Bivariate polynomial factorization is an important stage of algebraic soft-decision decoding of Reed-Solomon (RS) codes and contributes to a significant portion of the overall decoding latency. With the exhaustive search-based root computation method, factorization latency is dominated by the root computation step, especially for RS codes defined over very large finite fields. The root-order prediction method proposed by Zhang and Parhi only improves average latency, but does not have any effect on the worst-case latency of the factorization procedure. Thus, neither approach is well-suited for delay-sensitive applications. In this paper, a novel architecture based on direct root computation is proposed to greatly reduce the factorization latency. Direct root computation is feasible because in most practical applications of algebraic soft-decision decoding of RS codes, enough decoding gain can be achieved with a relatively low interpolation cost, which results in a bivariate polynomial with low Y-degree. Compared with existing works, not only does the new architecture have a significantly smaller worst-case decoding latency, but it is also more area efficient since the corresponding hardware for routing polynomial coefficients is eliminated. 相似文献
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Huffman W.C. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1990,36(3):651-660
A general decomposition theorem is given for self-dual codes over finite fields that have a permutation automorphism of a given form. Such a code can be decomposed as a direct sum of subcodes that may be viewed as shorter-length codes over extension fields where the dual of each direct summand is also a direct summand. Situations in which it is easy to distinguish such codes are also presented. These results are used to enumerate some of the extremal quaternary self-dual codes of lengths 18, 20, 22, 26 and 28 相似文献
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《IEEE transactions on circuits and systems. I, Regular papers》2008,55(10):3050-3062
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Recently, we have developed a new framework to study error-control coding using finite-field wavelets and filterbanks (FBs). This framework reveals a rich set of signal processing techniques that can be exploited to investigate new error correcting codes and to simplify encoding and decoding techniques for some existing ones. The paper introduces the theory of wavelet decompositions of signals in vector spaces defined over Galois fields. To avoid the limitations of the number theoretic Fourier transform, our wavelet transform relies on a basis decomposition in the time rather than the frequency domain. First, by employing a symmetric, nondegenerate canonical bilinear form, we obtain a necessary and sufficient condition that the basis functions defined over finite fields must satisfy in order to construct an orthogonal wavelet transform. Then, we present a design methodology to generate the mother wavelet and scaling function over finite fields by relating the wavelet transform to two-channel paraunitary (PU) FBs. Finally, we describe the application of this transform to the construction of error correcting codes. In particular, we give examples of double circulant codes that are generated by wavelets. 相似文献
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Lin J. Sha J. Wang Z. Li L. 《Circuits and Systems II: Express Briefs, IEEE Transactions on》2010,57(1):51-55
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Jiun Shiu Ja-Ling Wu 《Communications, IEEE Transactions on》1996,44(3):281-283
A majority decoding algorithm for a class of real-number codes is presented. Majority decoding has been a relatively simple and fast decoding technique for codes over finite fields. When applied to decode real-number codes, the robustness of the majority decoding to the presence of background noise, which is usually an annoying problem for existing decoding algorithms for real-number codes, is its most prominent property. The presented class of real-number codes has generator matrices similar to those of the binary Reed-Muller codes and is decoded by similar majority logic 相似文献
14.
We introduce a wide class of low-density parity-check (LDPC) codes, large enough to include LDPC codes over finite fields, rings, or groups, as well as some nonlinear codes. A belief-propagation decoding procedure with the same complexity as for the decoding of LDPC codes over finite fields is also presented. Moreover, an encoding procedure is developed 相似文献
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Reed-Solomon (RS) codes are among the most widely utilized error-correcting codes in digital communication and storage systems. Among the decoding algorithms of RS codes, the recently developed Koetter-Vardy (KV) soft-decision decoding algorithm can achieve substantial coding gain, while has a polynomial complexity. One of the major steps of the KV algorithm is the factorization. Each iteration of the factorization mainly consists of root computations over finite fields and polynomial updating. To speed up the factorization step, a fast factorization architecture has been proposed to circumvent the exhaustive-search-based root computation from the second iteration level by using a root-order prediction scheme. Based on this scheme, a partial parallel factorization architecture was proposed to combine the polynomial updating in adjacent iteration levels. However, in both of these architectures, the root computation in the first iteration level is still carried out by exhaustive search, which accounts for a significant part of the overall factorization latency. In this paper, a novel iterative prediction scheme is proposed for the root computation in the first iteration level. The proposed scheme can substantially reduce the latency of the factorization, while only incurs negligible area overhead. Applying this scheme to a (255, 239) RS code, speedups of 36% and 46% can be achieved over the fast factorization and partial parallel factorization architectures, respectively. 相似文献
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Dan Tang 《电子科技学刊:英文版》2016,14(1):43-48
In the process of encoding and decoding, erasure codes over binary fields, which just need AND operations and XOR operations and therefore have a high computational efficiency, are widely used in various fields of information technology. A matrix decoding method is proposed in this paper. The method is a universal data reconstruction scheme for erasure codes over binary fields. Besides a pre-judgment that whether errors can be recovered, the method can rebuild sectors of loss data on a fault-tolerant storage system constructed by erasure codes for disk errors. Data reconstruction process of the new method has simple and clear steps, so it is beneficial for implementation of computer codes. And more, it can be applied to other non-binary fields easily, so it is expected that the method has an extensive application in the future. 相似文献
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Fekri F. Mersereau R.M. Schafer R.W. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2002,48(11):2964-2979
Motivated by our wavelet framework for error-control coding, we proceed to develop an important family of wavelet transforms over finite fields. Paraunitary (PU) filter banks that are realizations of orthogonal wavelets by multirate filters are an important subclass of perfect reconstruction (PR) filter banks. A parameterization of PU filter banks that covers all possible PU systems is very desirable in error-control coding because it provides a framework for optimizing the free parameters to maximize coding performance. This paper undertakes the problem of classifying all PU matrices with entries from a polynomial ring, where the coefficients of the polynomials are taken from finite fields. It constructs Householder transformations that are used as elementary operations for the realization of all unitary matrices. Then, it introduces elementary PU building blocks and a factorization technique that is specialized to obtain a complete realization for all PU filter banks over fields of characteristic two. This is proved for the 2 × 2 case, and conjectured for the M × M case, where M ⩾ 3. Using these elementary building blocks, we can construct all PU filter banks over fields of characteristic two. These filter banks can be used to implement transforms which, in turn, provide a powerful new perspective on the problems of constructing and decoding arbitrary-rate error-correcting codes 相似文献
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低密度校验(Low-Density Parity-Check)码作为迄今为止性能最好的纠错码之一, 目前已经被许多数字通信标准广泛采用。伪随机低密度校验码(Pseudo-Random)是 LDPC 码的一个子类,已被应用于空间通信和无线网络技术。本文给出了一种基于有限域的伪随机 LDPC 码构造方法,并采用理论分析和仿真结果分析相结合的方法,对伪随机 LDPC 码的构造和编译码方法进行了研究,并给出了实现中适合的译码算法及量化方案。 相似文献