Z_p^(k+1)环上的Quasi-Cyclic码

近年来,剩余类环Zm上的编码理论有很大的发展,人们通过Gray映射建立了比较系统的Zm环上的编码理论。文章定义了对于n=n1pδ,环Zn1pk+1到环Zppkn1上的Gray映射,给出了该映射的几个性质,并由此得出了Zpk+1环上的指数为pδt长为n=pδn1的quasi_cyclic码与Zp环上的quasi_cyclic码的一一对应关系,这里的t|n1,(n1,p)=1,从而环Zpk+1上的quasi_cyclic码可以看作是环Zp上的quasi_cyclic码,也即看作是有限素域上的quasi_cyclic码。

DESIGN OF QUASI-CYCLIC LDPC CODES BASED ON EUCLIDEAN GEOMETRIES

A new method for constructing Quasi-Cyclic (QC) Low-Density Parity-Check (LDPC) codes based on Euclidean Geometry (EG) is presented. The proposed method results in a class of QC-LDPC codes with girth of at least 6 and the designed codes perform very close to the Shannon limit with iterative decoding. Simulations show that the designed QC-LDPC codes have almost the same performance with the existing EG-LDPC codes.

Combinatorial design-based quasi-cyclic LDPC codes with girth eight

This paper presents a novel regular Quasi-Cyclic (QC)Low Density Parity Check (LDPC)codes with columnweight three and girth at least eight.These are designed on the basis of combinatorial design in which subsets applied for the construction of circulant matrices are determined by a particular subset.Considering the nonexistence of cycles four and six in the structure of the parity check matrix,a bound for their minimum weight is proposed.The simtdations conducted confirm that without applying a masking technique,the newly implemented codes have a performance similar to or better than other well-known codes.This is evident in the waterfall region, while their error floor at very low Bit Error Rate (BER)is expected.

On the Girth of Tanner (5,7) Quasi-Cyclic LDPC Codes

The girth plays an important role in the design of LDPC codes. In order to determine the girth of Tanner(5,7) quasi-cyclic( QC) LDPC codes with length 7p for p being a prime with the form 35 m + 1,the cycles of lengths 4,6,8,and 10 are analyzed. Then these cycles are classified into sixteen categories,each of which can be expressed as an ordered block sequence,or a certain type. It is also shown that the existence of these cycles is equal to polynomial equations over Fpwho has a 35th unit root. We check if these polynomial equations have a 35th unit root and obtain the girth values of Tanner(5,7) QC LDPC codes.

Quasi-cyclic Random Projection Code and Hardware Implementation

Random Projection Code (RPC) is a mechanism that combines channel coding and modulation together and realizes rate adaptation in the receiving end. Random projection code’s mapping matrix has significant influences on decoding performance as well as hardware implementation complexity. To reduce hardware implementation complexity, we design a quasi-cyclic mapping matrix for RPC codes. Compared with other construction approaches, our design gets rid of data filter component, thus reducing chip area 7284.95 um2, and power consumption 331.46 uW in 0.13 um fabrication. Our simulation results show that our method does not cause any performance loss and even gets 0.2 dB to 0.5 dB gain at BER 10-4.

Quasi-Cyclic LDPC环优化构造算法

本文研究了准循环LDPC码的一致校验矩阵与其对应Tanner图环结构之间的关系,将局部平均围长优化算法引入优化构造算法中,提出了一种基于PEG算法的准循环扩展LDPC码构造的改进算法。在改进算法中,首先利用PEG算法产生基矩阵,然后基于平均围长最大准则选择循环移位置换矩阵对基矩阵进行准循环扩展,通过围长分布的优化,从而改善了迭代译码的性能。仿真结果表明,在码长相同、码率和度分布近似情况下,与文献[7]中基于PEG算法的准循环扩展构造的码字比较,改进算法构造的码字能够获得更加优异的性能。

Quantum quasi-cyclic low-density parity-check error-correcting codes

In this paper, we propose the approach of employing circulant permutation matrices to construct quantum quasi-cyclic (QC) low-density parity-check (LDPC) codes. Using the proposed approach one may construct some new quantum codes with various lengths and rates of no cycles-length 4 in their Tanner graphs. In addition, these constructed codes have the advantages of simple implementation and low-complexity encoding. Finally, the decoding approach for the proposed quantum QC LDPC is investigated.

Quaternary quasi-cyclic codes

Quasi-cyclic codes of length mn over Z4 are shown to be equivalent to A-submodules of An,where A = Z4 x /(xm -1).In the case of m being odd,all quasi-cyclic codes are shown to be decomposable into the direct sum of a fixed number of cyclic irreducible A-submodules.Finally the distinct quasi-cyclic codes as well as some specific subclasses are enumerated.

Quasi-cyclic LDPC codes with high-rate and low error floor based on Euclidean geometries

An improved Euclidean geometry approach to design quasi-cyclic(QC) Low-density parity-check(LDPC) codes with high-rate and low error floor is presented.The constructed QC-LDPC codes with high-rate have lower error floor than the original codes.The distribution of the minimum weight codeword is analyzed,and a sufficient existence condition of the minimum weight codeword is found.Simulations show that a lot of QC-LDPC codes with lower error floor can be designed by reducing the number of the minimum weight codewords satisfying this sufficient condition.

1-GENERATOR QUASI-CYCLIC CODES

这篇论文讨论 1 发电机的枚举伪周期的代码；描述将获得一个的一个算法，；仅仅，为每 1 发电机的生成器伪周期的代码。

Design and Efficient Hardware Implementation Schemes for Non-Quasi-Cyclic LDPC Codes

The design of a high-speed decoder using traditional partly parallel architecture for Non-Quasi-Cyclic(NQC) Low-Density Parity-Check(LDPC) codes is a challenging problem due to its high memory-block cost and low hardware utilization efficiency. In this paper, we present efficient hardware implementation schemes for NQCLDPC codes. First, we propose an implementation-oriented construction scheme for NQC-LDPC codes to avoid memory-access conflict in the partly parallel decoder. Then, we propose a Modified Overlapped Message-Passing(MOMP) algorithm for the hardware implementation of NQC-LDPC codes. This algorithm doubles the hardware utilization efficiency and supports a higher degree of parallelism than that used in the Overlapped Message Passing(OMP) technique proposed in previous works. We also present single-core and multi-core decoder architectures in the proposed MOMP algorithm to reduce memory cost and improve circuit efficiency. Moreover, we introduce a technique called the cycle bus to further reduce the number of block RAMs in multi-core decoders. Using numerical examples, we show that, for a rate-2/3, length-15360 NQC-LDPC code with 8.43-d B coding gain for Binary PhaseShift Keying(BPSK) in an Additive White Gaussian Noise(AWGN) channel, the decoder with the proposed scheme achieves a 23.8%–52.6% reduction in logic utilization per Mbps and a 29.0%–90.0% reduction in message-memory bits per Mbps.

Code Design and Shuffled Iterative Decoding of a Quasi-Cyclic LDPC Coded OFDM System

In multipath environments, the error rate performance of orthogonal frequency division multiplexing (OFDM) is severely degraded by the deep fading subcarriers. Powerful error-correcting codes must be used with OFDM. This paper presents a quasi-cyclic low-density parity-check (LDPC) coded OFDM system, in which the redundant bits of each codeword are mapped to a higher-order modulation constellation. The optimal degree distribution was calculated using density evolution. The corresponding quasi-cyclic LDPC code was then constructed using circulant permutation matrices. Group shuffled message passing scheduling was used in the iterative decoding. Simulation results show that the system achieves better error rate performance and faster decoding convergence than conventional approaches on both additive white Gaussian noise (AWGN) and Rayleigh fading channels.

双层圆钢管混凝土长柱压扭滞回性能试验

为研究双层圆钢管混凝土长柱在压、扭荷载作用下的力学性能,利用研制的Stewart六自由度加载平台,进行了两个普通圆钢管混凝土长柱和两个双层圆钢管混凝土长柱试件在纯扭、压扭作用下的低周往复试验。对比分析了各试件的承载力、扭转变形、耗能、滞回性能,进行了有限元参数分析。研究表明:普通圆钢管混凝土长柱和双层圆钢管混凝土长柱均具有较好的抗扭能力;与普通圆钢管混凝土长柱相比,双层圆钢管混凝土长柱的初始刚度和承载力略有提升,滞回曲线更饱满,耗能能力和延性大幅提升;参数分析表明含钢率一定时,内层钢管径厚比越大,对抗扭越有利;一定范围内的轴向荷载,可提高钢管混凝土柱的抗扭能力。

基于双序列反序的(4,L)规则girth-8 QC-LDPC短码

围长较大的短码长准循环(QC)低密度奇偶校验(LDPC)码的显式构造对于QC-LDPC短码的理论研究与工程应用具有重要意义。首先提出一种基于成对策略的贪婪搜索算法,并根据此算法在列重J为4时的经验结果,归纳总结出一种具有双序列反序特征的指数矩阵。随后证明了该指数矩阵对于任意行重L均对应于围长为8的QC-LDPC码。与现有的典型显式构造方法即最大公约数(GCD)方法相比,新QC-LDPC码提供的码长显著降低。最后,将指数矩阵的拆分拼接和掩膜处理技巧与新QC-LDPC码结合起来,设计出了译码性能在高信噪比区超过5G NR LDPC码的合成码。

基于Stanley序列的QC-LDPC码新颖构造方法

针对准循环低密度奇偶校验(quasi-cyclic low-density parity-check,QC-LDPC)码的短环结构会严重影响码字纠错性能的问题,基于Stanley序列(Stanley sequence,SS)提出一种围长至少为8的QC-LDPC码新颖构造方法。从Stanley序列中选取某些特定元素构成一个呈递增关系的集合,利用穷举算法搜索出满足无环4和环6条件的元素得到另一个递增集合,构造相应的指数矩阵,得到其奇偶校验矩阵。仿真结果表明,在误码率(bit error rate,BER)为10-6时,所构造的SS-QC-LDPC码与同码率码长的其他QC-LDPC码码型相比,其净编码增益均有一定提升,因而其纠错性能较好,且无错误平层现象。此外,该构造方法的计算复杂度较低。

Low-Density Parity-Check Codes:Highway to Channel Capacity

Low-density parity-check(LDPC)codes are not only capacity-approaching,but also greatly suitable for high-throughput implementation.Thus,they are the most popular codes for high-speed data transmission in the past two decades.Thanks to the low-density property of their parity-check matrices,the optimal maximum a posteriori probability decoding of LDPC codes can be approximated by message-passing decoding with linear complexity and highly parallel nature.Then,it reveals that the approximation has to carry on Tanner graphs without short cycles and small trapping sets.Last,it demonstrates that well-designed LDPC codes with the aid of computer simulation and asymptotic analysis tools are able to approach the channel capacity.Moreover,quasi-cyclic(QC)structure is introduced to significantly facilitate their high-throughput implementation.In fact,compared to the other capacity-approaching codes,QC-LDPC codes can provide better area-efficiency and energy-efficiency.As a result,they are widely applied in numerous communication systems,e.g.,Landsat satellites,Chang’e Chinese Lunar mission,5G mobile communications and so on.What’s more,its extension to non-binary Galois fields has been adopted as the channel coding scheme for BeiDou navigation satellite system.

基于原模图的8环QC-LDPC码构造方法

针对当前准循环低密度奇偶校验(Quasi-Cyclic Low-Density Parity-Check,QC-LDPC)码存在短环及纠错性能不够好的问题,基于原模图提出一种新颖的QC-LDPC码构造方法。该方法选择码长码率可灵活调整的原模图作为基矩阵,再结合具有特殊性质的卢卡斯数列和等差数列,通过原模图的低译码门限和数列的特殊性质,构造校验矩阵环长至少为8,且所需存储空间少,易于硬件实现。仿真结果表明:该方法构造的PLA-QC-LDPC(2400,1200)码与同等码长码率中基于卢卡斯数列和最大公约数序列的可快速编码的非规则LG-QC-LDPC码、基于素数和乘法表构造的PM-QC-LDPC码以及基于原模图和消除基本陷阱集的非规则PL-QC-LDPC码相比,净编码增益均有一定程度的提高。

基于基矩阵排列优化算法的非规则准循环低密度奇偶校验码构造

为了提升非规则准循环低密度奇偶校验(QC-LDPC)码的误码率性能、降低构造算法的复杂度,该文提出一种基于基矩阵排列优化算法的非规则QC-LDPC码构造方法。首先,利用基于外部信息传递(EXIT)图的阈值分析算法得到满足码率和列重要求的非规则QC-LDPC码的最优度分布,然后将围长和短环数量作为新的约束条件对具有最优度分布的码集进行分析,得到具有最优度分布和最少短环数量的最优基矩阵排列结构,最后,根据得到的基矩阵对规则指数矩阵进行置零操作得到目标非规则QC-LDPC码。该构造方法相对于随机构造方法具有更低的实现复杂度,同时可以通过改变算法的参数值实现码长和码率的灵活设计。仿真结果表明,与现有的一些构造方法相比,所提方法构造的非规则QC-LDPC码在加性高斯白噪声(AWGN)信道上具有更好的误码率性能。

关于全循环数的性质及其相关数之间的相互关系的研究

本文提出了准全循环数的概念,给出了全循环数的性质,并以全循环数142857为例,详细讨论了它与相关数之间的关系。最后提出了142857为最完美的全循环数,给出了若干推论。

叙述跨层艺术研究的中国之路

中国文艺作品中的叙述跨层技巧源远流长,为作品带来奇幻、悬疑等独特的艺术效果。在叙述跨层理论三十余年的建构过程中,中国学者走出了一条深具中国特色的研究道路:首先,创造了中国叙述学自己的叙述跨层术语群,并发掘出了中国文学作品中的回旋分层形式;其次,建构了多种媒介和体裁视域下叙述跨层的分析框架,并将其纳入艺术的“准不可能世界”理论中;更为重要的是,跨层艺术的思想渊源被植根于中国文化的元意识传统之中。中国式叙述跨层理论体系的建立为跨层艺术的传承与发展奠定了基础。