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LDPC block and convolutional codes based on circulant matrices 总被引:18,自引:0,他引:18
Tanner R.M. Sridhara D. Sridharan A. Fuja T.E. Costello D.J. Jr. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2004,50(12):2966-2984
A class of algebraically structured quasi-cyclic (QC) low-density parity-check (LDPC) codes and their convolutional counterparts is presented. The QC codes are described by sparse parity-check matrices comprised of blocks of circulant matrices. The sparse parity-check representation allows for practical graph-based iterative message-passing decoding. Based on the algebraic structure, bounds on the girth and minimum distance of the codes are found, and several possible encoding techniques are described. The performance of the QC LDPC block codes compares favorably with that of randomly constructed LDPC codes for short to moderate block lengths. The performance of the LDPC convolutional codes is superior to that of the QC codes on which they are based; this performance is the limiting performance obtained by increasing the circulant size of the base QC code. Finally, a continuous decoding procedure for the LDPC convolutional codes is described. 相似文献
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Construction of nonbinary cyclic, quasi-cyclic and regular LDPC codes: a finite geometry approach 总被引:1,自引:0,他引:1
Lingqi Zeng Lan Lan Ying Yu Tai Bo Zhou Shu Lin Abdel-Ghaffar K.A.S. 《Communications, IEEE Transactions on》2008,56(3):378-387
This paper presents five methods for constructing nonbinary LDPC codes based on finite geometries. These methods result in five classes of nonbinary LDPC codes, one class of cyclic LDPC codes, three classes of quasi-cyclic LDPC codes and one class of structured regular LDPC codes. Experimental results show that constructed codes in these classes decoded with iterative decoding based on belief propagation perform very well over the AWGN channel and they achieve significant coding gains over Reed-Solomon codes of the same lengths and rates with either algebraic hard-decision decoding or Kotter-Vardy algebraic soft-decision decoding at the expense of a larger decoding computational complexity. 相似文献
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Low-density parity-check codes based on finite geometries: arediscovery and new results 总被引:3,自引:0,他引:3
Kou Y. Lin S. Fossorier M.P.C. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2001,47(7):2711-2736
This paper presents a geometric approach to the construction of low-density parity-check (LDPC) codes. Four classes of LDPC codes are constructed based on the lines and points of Euclidean and projective geometries over finite fields. Codes of these four classes have good minimum distances and their Tanner (1981) graphs have girth 6. Finite-geometry LDPC codes can be decoded in various ways, ranging from low to high decoding complexity and from reasonably good to very good performance. They perform very well with iterative decoding. Furthermore, they can be put in either cyclic or quasi-cyclic form. Consequently, their encoding can be achieved in linear time and implemented with simple feedback shift registers. This advantage is not shared by other LDPC codes in general and is important in practice. Finite-geometry LDPC codes can be extended and shortened in various ways to obtain other good LDPC codes. Several techniques of extension and shortening are presented. Long extended finite-geometry LDPC codes have been constructed and they achieve a performance only a few tenths of a decibel away from the Shannon theoretical limit with iterative decoding 相似文献
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Lingqi Zeng Lan Lan Tai Y.Y. Shumei Song Shu Lin Abdel-Ghaffar K. 《Communications, IEEE Transactions on》2008,56(4):545-554
This paper is concerned with construction of efficiently encodable nonbinary quasi-cyclic LDPC codes based on finite fields. Four classes of nonbinary quasi-cyclic LDPC codes are constructed. Experimental results show that codes constructed perform well with iterative decoding using a fast Fourier transform based q-ary sum-product algorithm and they achieve significant coding gains over Reed-Solomon codes of the same lengths and rates decoded with either algebraic hard- decision Berlekamp-Massey algorithm or algebraic soft-decision Kotter-Vardy algorithm. 相似文献
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This paper presents algebraic methods for constructing high performance and efficiently encodable non-binary quasi-cyclic LDPC codes based on flats of finite Euclidean geometries and array masking. Codes constructed based on these methods perform very well over the AWGN channel. With iterative decoding using a Fast Fourier Transform based sum-product algorithm, they achieve significantly large coding gains over Reed-Solomon codes of the same lengths and rates decoded with either algebraic hard-decision Berlekamp-Massey algorithm or algebraic soft-decision K?tter-Vardy algorithm. Due to their quasi-cyclic structure, these non-binary LDPC codes on Euclidean geometries can be encoded using simple shiftregisters with linear complexity. Structured non-binary LDPC codes have a great potential to replace Reed-Solomon codes for some applications in either communication or storage systems for combating mixed types of noise and interferences. 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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Zhang J. Fossorier M. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2006,52(7):3168-3185
In this paper, the mean field (MF) and mixed mean field (MMF) algorithms for decoding low-density parity-check (LDPC) codes are considered. The MF principle is well established in statistical physics and artificial intelligence. Instead of using a single completely factorized approximated distribution as in the MF approach, the mixed MF algorithm forms a weighted average of several MF distributions as an approximation of the true posterior probability distribution. The MF decoding algorithm for linear block codes is derived and shown to be an approximation of the a posteriori probability (APP) decoding algorithm. The MF approach is then developed in the context of iterative decoding and presented as an approximation of the popular belief propagation decoding method. These results are extended to iterative decoding with the MMF algorithm. Simulation results show that the MF and MMF decoding algorithms yield a good performance-complexity tradeoff, especially when employed for decoding LDPC codes based on finite geometries. 相似文献
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Codes on finite geometries 总被引:5,自引:0,他引:5
Tang H. Xu J. Lin S. Abdel-Ghaffar K.A.S. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2005,51(2):572-596
New algebraic methods for constructing codes based on hyperplanes of two different dimensions in finite geometries are presented. The new construction methods result in a class of multistep majority-logic decodable codes and three classes of low-density parity-check (LDPC) codes. Decoding methods for the class of majority-logic decodable codes, and a class of codes that perform well with iterative decoding in spite of having many cycles of length 4 in their Tanner graphs, are presented. Most of the codes constructed can be either put in cyclic or quasi-cyclic form and hence their encoding can be implemented with linear shift registers. 相似文献
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《AEUE-International Journal of Electronics and Communications》2014,68(5):379-383
Quasi-cyclic (QC) low-density parity-check (LDPC) codes have the parity-check matrices consisting of circulant matrices. Since QC LDPC codes whose parity-check matrices consist of only circulant permutation matrices are difficult to support layered decoding and, at the same time, have a good degree distribution with respect to error correcting performance, adopting multi-weight circulant matrices to parity-check matrices is useful but it has not been much researched. In this paper, we propose a new code structure for QC LDPC codes with multi-weight circulant matrices by introducing overlapping matrices. This structure enables a system to operate on dual mode in an efficient manner, that is, a standard QC LDPC code is used when the channel is relatively good and an enhanced QC LDPC code adopting an overlapping matrix is used otherwise. We also propose a new dual mode parallel decoder which supports the layered decoding both for the standard QC LDPC codes and the enhanced QC LDPC codes. Simulation results show that QC LDPC codes with the proposed structure have considerably improved error correcting performance and decoding throughput. 相似文献
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Sason I. Urbanke R. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2003,49(7):1611-1635
We derive lower bounds on the density of parity-check matrices of binary linear codes which are used over memoryless binary-input output-symmetric (MBIOS) channels. The bounds are expressed in terms of the gap between the rate of these codes for which reliable communications is achievable and the channel capacity; they are valid for every sequence of binary linear block codes if there exists a decoding algorithm under which the average bit-error probability vanishes. For every MBIOS channel, we construct a sequence of ensembles of regular low-density parity-check (LDPC) codes, so that an upper bound on the asymptotic density of their parity-check matrices scales similarly to the lower bound. The tightness of the lower bound is demonstrated for the binary erasure channel by analyzing a sequence of ensembles of right-regular LDPC codes which was introduced by Shokrollahi, and which is known to achieve the capacity of this channel. Under iterative message-passing decoding, we show that this sequence of ensembles is asymptotically optimal (in a sense to be defined in this paper), strengthening a result of Shokrollahi. Finally, we derive lower bounds on the bit-error probability and on the gap to capacity for binary linear block codes which are represented by bipartite graphs, and study their performance limitations over MBIOS channels. The latter bounds provide a quantitative measure for the number of cycles of bipartite graphs which represent good error-correction codes. 相似文献
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有限平面LDPC码是一类重要的有结构的LDPC码,在利用和积算法(SPA)等迭代译码方法进行译码时表现出卓越的纠错性能。众所周知,次优的迭代译码不是最大似然译码,因而如何对迭代译码的性能进行理论分析一直是LDPC码的核心问题之一。近几年来,Tanner图上的停止集(stopping set)和停止距离(stopping distance)由于其在迭代译码性能分析中的重要作用而引起人们的重视。该文通过分析有限平面LDPC码的停止集和停止距离,从理论上证明了有限平面LDPC码的最小停止集一定是最小重量码字的支撑,从而对有限平面LDPC码在迭代译码下的良好性能给出了理论解释。 相似文献
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The most powerful channel-coding schemes, namely, those based on turbo codes and low-density parity-check (LDPC) Gallager codes, have in common the principle of iterative decoding. However, the relative coding structures and decoding algorithms are substantially different. This paper shows that recently proposed novel coding structures bridge the gap between these two schemes. In fact, with properly chosen component convolutional codes, a turbo code can be successfully decoded by means of the decoding algorithm used for LDPC codes, i.e., the belief-propagation algorithm working on the code Tanner graph. These new turbo codes are here nicknamed "turbo Gallager codes." Besides being interesting from a conceptual viewpoint, these schemes are important on the practical side because they can be decoded in a fully parallel manner. In addition to the encoding complexity advantage of turbo codes, the low decoding complexity allows the design of very efficient channel-coding schemes. 相似文献
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提出了基于均衡不完全区组设计(Balanced Incomplete Block Design,BIBD)的多进制准循环LDPC(Low-Density Parity-Check)码代数构造方法。在该构造方法中提出了广义多进制位置向量的概念,并根据广义多进制位置向量和BIBD法对指数矩阵进行广义二维扩展,构造出具有循环置换子矩阵的多进制校验矩阵,由此得到girth不小于6的多进制LDPC码。仿真结果表明,采用FFT-QSPA(基于快速傅里叶变换的多进制和积算法)对构造出的LDPC码进行译码,在AWGN信道下相比于同参数的RS码来说可以取得明显的编码增益,并且优于多进制Mackay码。 相似文献
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Heng Tang Jun Xu Yu Kou Lin S. Abdel-Ghaffar K. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2004,50(6):1269-1279
This correspondence presents three algebraic methods for constructing low-density parity-check (LDPC) codes. These methods are based on the structural properties of finite geometries. The first method gives a class of Gallager codes and a class of complementary Gallager codes. The second method results in two classes of circulant-LDPC codes, one in cyclic form and the other in quasi-cyclic form. The third method is a two-step hybrid method. Codes in these classes have a wide range of rates and minimum distances, and they perform well with iterative decoding. 相似文献
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This paper develops codes suitable for iterative decoding using the sum-product algorithm. By considering a large class of combinatorial structures, known as partial geometries, we are able to define classes of low-density parity-check (LDPC) codes, which include several previously known families of codes as special cases. The existing range of algebraic LDPC codes is limited, so the new families of codes obtained by generalizing to partial geometries significantly increase the range of choice of available code lengths and rates. We derive bounds on minimum distance, rank, and girth for all the codes from partial geometries, and present constructions and performance results for the classes of partial geometries which have not previously been proposed for use with iterative decoding. We show that these new codes can achieve improved error-correction performance over randomly constructed LDPC codes and, in some cases, achieve this with a significant decrease in decoding complexity. 相似文献
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Gil Wiechman Igal Sason 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2007,53(2):550-579
The moderate complexity of low-density parity-check (LDPC) codes under iterative decoding is attributed to the sparseness of their parity-check matrices. It is therefore of interest to consider how sparse parity-check matrices of binary linear block codes can be a function of the gap between their achievable rates and the channel capacity. This issue was addressed by Sason and Urbanke, and it is revisited in this paper. The remarkable performance of LDPC codes under practical and suboptimal decoding algorithms motivates the assessment of the inherent loss in performance which is attributed to the structure of the code or ensemble under maximum-likelihood (ML) decoding, and the additional loss which is imposed by the suboptimality of the decoder. These issues are addressed by obtaining upper bounds on the achievable rates of binary linear block codes, and lower bounds on the asymptotic density of their parity-check matrices as a function of the gap between their achievable rates and the channel capacity; these bounds are valid under ML decoding, and hence, they are valid for any suboptimal decoding algorithm. The new bounds improve on previously reported results by Burshtein and by Sason and Urbanke, and they hold for the case where the transmission takes place over an arbitrary memoryless binary-input output-symmetric (MBIOS) channel. The significance of these information-theoretic bounds is in assessing the tradeoff between the asymptotic performance of LDPC codes and their decoding complexity (per iteration) under message-passing decoding. They are also helpful in studying the potential achievable rates of ensembles of LDPC codes under optimal decoding; by comparing these thresholds with those calculated by the density evolution technique, one obtains a measure for the asymptotic suboptimality of iterative decoding algorithms 相似文献