光通信系统中一种新颖的满秩QC-LDPC码的构造方法研究

为使低密度奇偶校验(LDPC)码高效地应用于光通信系统中,针对光通信系统的传输特点,提出了一种新颖的基于循环置换矩阵和掩蔽矩阵构造满秩准循环低密度奇偶校验(QC-LDPC)码的方法。该方法定义了一类基矩阵,由基矩阵扩展出循环置换矩阵,构造出围长至少为8的校验矩阵;提出了掩蔽矩阵的设计规则,并利用设计的掩蔽矩阵对前面得到的校验矩阵进行变换,构造出围长至少为8的满秩QC-LDPC码。与多种不同的QC-LDPC码构造方法进行理论分析和性能仿真比较,结果表明,利用该方法构造出的LDPC码字是满秩的,具有严格的准循环特性和优异的纠错性能,且构造灵活。该方法构造的码字适用于光通信系统。     

围长至少为8的QC-LDPC码的新构造:一种显式框架

 构造围长较大的校验矩阵,是提高二进制和多进制QC-LDPC码译码性能的一种有效手段.本文提出一种不需要借助于任何计算机搜索步骤,能够直接构造出围长至少为8的QC-LDPC码的显式构造框架.该框架所构造的QC-LDPC码不仅满足围长至少为8的条件,而且还具有循环置换矩阵(CPM)尺寸可以连续变化的优点.该框架可以分为两个步骤:第一步是在无穷大CPM尺寸条件下利用确定性方法构造一个围长至少为8的校验矩阵;第二步是根据本文新发现的一个围长性质,从该校验矩阵的移位矩阵直接精确地计算出CPM尺寸连续变化的紧致下界.     

一种高性能低复杂度的非规则LDPC码的构造方法

该文提出了一种基于置换矩阵(permutation matrix)的非规则低密度奇偶校验(LDPC)码构造方法。首先,提出了基于改进eIRA(IeIRA)算法的全局矩阵M;接着,通过对全局矩阵H进行矩阵置换,生成LDPC码的校验矩阵H;研究了校验矩H中短圈(short cycle)长度与置换矩阵循环移位系数的关系,通过选择循环移位系数,以达到改善误比特率性能的目的。仿真结果表明,该文提出的构造方法在保证线性编码复杂度的前提下,增大了码字的最小距离,减少了小停止集合(stopping set)的数量,降低了误比特率的差错平台(error floor)(达到10-9)。     

一种改进的基于中国剩余定理的QC-LDPC码构造方法

为增大QC-LDPC码围长的同时减少码中包含的短环,提高其纠错性能,提出了一种基于中国剩余定理( CRT)的QC-LDPC码改进联合构造方法。该方法将设计围长为g的长码长的QC-LD-PC码的问题简化为设计一个围长为g的短分量码的问题,然后通过对其余分量码校验矩阵的列块进行适当置换,使得构造出的QC-LDPC码具有更少的短环和更优的性能,更适于可靠性要求较高的通信系统。仿真结果表明,与已有的CRT联合构造方法设计的QC-LDPC码相比,新方法构造的QC-LDPC码具有更少的短环,在误码率为10-6时获得了1.2 dB的编码增益。     

利用完备差集构造QC-LDPC码

针对准循环低密度奇偶校验( QC-LDPC)码中循环置换矩阵的移位次数的确定问题,提出了一种利用组合设计中完备差集( PDF)构造QC-LDPC码的新颖方法。当循环置换矩阵的维度大于一定值时,该方法所构造的规则QC-LDPC码围长至少为6,具有灵活选择码长和码率的优点,且所需的存储空间更少,降低了硬件实现的复杂度。仿真结果表明：在误码率为10-5时,所构造的码率为3/4的PDF-QC-LDPC(3136,2352)与基于最大公约数(GCD)构造的GCD-QC-LDPC(3136,2352)码和基于循环差集(CDF)构造的CDF-QC-LDPC(3136,2352)码相比,其净编码增益(NCG)分别有0.41 dB和0.32 dB的提升;且在码率为4/5时,所构造的PDF-QC-LDPC (4880,3584)码比GCD-QC-LDPC(4880,3584)码和CDF-QC-LDPC(4880,3584)码的NCG分别改善了0.21 dB和0.13 dB。     

不规则LDPC码面向4G的性能改进

基于4G和WiMAX在技术发展方向上的融合,对IEEE 802.16e标准推荐的由单位置换矩阵I构造的不规则QC-LDPC码,构造循环移位置换矩阵Q取代J矩阵填充奇偶校验矩阵H,仿真实验表明由Q矩阵取代I矩阵,能在一定程度上改善不规则QC-LDPC码的性能.     

编码协作系统准循环重复累积码的联合设计与性能分析

重复累积(RA)码是一种特殊结构的低密度奇偶校验(LDPC)码,不仅具有LDPC码的优点,还能实现差分编码。针对LDPC编码协作系统编码复杂度高、时延长的问题,该文引入准循环RA(QC-RA)码,推导出信源节点和中继节点采用的QC-RA码对应的联合校验矩阵,基于公差构造方法设计该联合校验矩阵,并证明该方法设计的联合校验矩阵不存在围长为girth-4, girth-6的短环。理论分析和仿真结果表明,同等条件下该系统比相应点对点系统具有更优异的误码率性能。仿真结果同时表明,与采用一般构造QC-RA码或基于Z型构造QC-RA码相比,采用基于公差构造的联合设计QC-RA码的多信源多中继协作均可获得更高的编码增益。     

编码协作系统准循环重复累积码的联合设计与性能分析

重复累积(RA)码是一种特殊结构的低密度奇偶校验(LDPC)码,不仅具有LDPC码的优点,还能实现差分编码。针对LDPC编码协作系统编码复杂度高、时延长的问题,该文引入准循环RA(QC-RA)码,推导出信源节点和中继节点采用的QC-RA码对应的联合校验矩阵,基于公差构造方法设计该联合校验矩阵,并证明该方法设计的联合校验矩阵不存在围长为girth-4, girth-6的短环。理论分析和仿真结果表明,同等条件下该系统比相应点对点系统具有更优异的误码率性能。仿真结果同时表明,与采用一般构造QC-RA码或基于Z型构造QC-RA码相比,采用基于公差构造的联合设计QC-RA码的多信源多中继协作均可获得更高的编码增益。     

任意列重大围长QC-LDPC码的确定性构造

针对准循环低密度奇偶校验（Quasi-Cyclic Low-Density Parity-Check,QC-LDPC）码中准循环基矩阵的移位系数确定问题,提出基于等差数列的确定方法.该方法构造的校验矩阵围长为8,列重可任意选取,移位系数由简单的数学表达式确定,编码复杂度与码长呈线性关系,节省了编解码存储空间.研究结果表明,列重和围长是影响码字性能的重要因素.在加性高斯白噪声（Additive White Gauss Noise,AWGN）信道和置信传播（Belief Propagation,BP）译码算法下,该方法构造的码字在短码时可以获得与IEEE 802.11n、802.16e码相一致的性能,在长码时误比特率性能接近DVB-S2码.同时表明该方法对码长和码率参数的设计具有较好的灵活性.     

光传输系统中基于Bose第一类方法对QC-LDPC码的一种新颖构造方法

基于平衡不完全区组设计(BIBD)、循环矩阵分解和循环置换矩阵,提出了一种适用于光传输系统的新颖准循环低密度奇偶校验码(QC-LDPC)构造方法。利用Bose的第一类方法构造的低密度校验矩阵对其进行循环列分解得到相应的模板矩阵,再利用合适的循环置换矩阵对其进行扩展。采用该方法构造的QC-LDPC码具有良好的结构,且可根据实际需要来灵活地选择码长和码率。仿真结果表明:在误码率为10-6时其码率均为93.7%的情况下,该方法构造的novel-QC-LDPC(10992,10305)码比ITU-T G.975中RS(255,239)码的净编码增益(NCG)改善了约1.8d B。因此该构造方法所构造的QC-LDPC码具有更好的纠错性能,更适合高速长距离的光传输系统。     

2-D DOA estimation employing L-shape array without estimation failure and pair matching failure

To remove estimation failure problems and pair matching failure problems in two-dimensional direction-of-arrival estimation, we propose a novel method employing a special L-shape array in this study. Two cross-correlated matrices can be used to complete two one-dimensional direction-of-arrival estimations. Based on array configuration and the definitions of azimuth and elevation angles, estimation in each dimension is completely independent. In this way, the estimation failure problems can be removed. Then, we calculate the estimation matrix and construct the expansion matrix of the steering matrix. Both the estimation matrix and the expansion matrix contain the ‘generalised’ permutation matrices. We use pair matching employing these ‘generalised’ permutation matrices instead of the ‘beamforming-like’ method. Simulation results verify that this algorithm can remove these problems and can also significantly improve performance without additional computational loads.     

针对 IRA-LDPC 码类的半随机半代数结构设计

提出用半随机半代数结构的设计方法来构造IRA-LDPC码的信息位所对应的奇偶校验矩阵H d。与现有结构化LDPC码相比,所给出的H d矩阵的结构化紧凑表示阵列的独特优势在于：可使H d矩阵中每个1元素的位置坐标均能用数学表达式计算得到,不仅极大地降低了随机奇偶校验矩阵对存储资源的消耗,而且还为LDPC编解码器的低复杂度硬件实现提供了可能性。与现有工业标准中的LDPC码相比,所提出的IRA-LDPC码在误码率与信噪比的仿真性能方面也占有优势。     

具有大码间距和大环路的QC-LDPC码的构造

本文总结了基于循环移位矩阵的QC-LDPC码的基矩阵和校验阵在维度、最小码间距和环路特性方面的关系.在此基础之上,本文提出了同时具有大的码间距和好的环路性能的QC-LDPC码的构造方法,首先构造了具有优化的维度分布和较大的最小码间距的基矩阵,再为基矩阵对应的模矩阵选择合适的循环偏移参数,从而构造了一类同时具有大码间距和...     

Scheduling reserved traffic in input-queued switches: new delay bounds via probabilistic techniques

We consider the problem of providing delay bounds to reserved traffic in high-speed input-queued switches. We assume that the matrix of bandwidth demands is known, and we use the now standard approach of decomposing this matrix into a convex combination of permutation matrices. Our problem, therefore, reduces to the problem of constructing a schedule for these permutation matrices. We derive delay bounds for four algorithms that are based on probabilistic techniques. For each algorithm, we first place tokens randomly in continuous time for each permutation matrix. If the nth token that appears corresponds to permutation matrix M/sub k/, then we schedule matrix M/sub k/ in the nth time slot. The algorithms differ in how the random token processes are defined. For two of the algorithms, we are able to perform a derandomization so as to obtain deterministic schedules. We show through numerical computation that in many situations the resulting delay bounds are smaller than the previously best-known delay bounds of Chang et al. (see Proc. IEEE IWQoS, London, U.K., 1999 and Proc. IEEE INFOCOM, Tel-Aviv, Israel, Mar 2000).     

Quasi-cyclic LDPC codes using overlapping matrices and their layered decoders

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.     

Shortened Array Codes of Large Girth

One approach to designing structured low-density parity-check (LDPC) codes with large girth is to shorten codes with small girth in such a manner that the deleted columns of the parity-check matrix contain all the variables involved in short cycles. This approach is especially effective if the parity-check matrix of a code is a matrix composed of blocks of circulant permutation matrices, as is the case for the class of codes known as array codes. We show how to shorten array codes by deleting certain columns of their parity-check matrices so as to increase their girth. The shortening approach is based on the observation that for array codes, and in fact for a slightly more general class of LDPC codes, the cycles in the corresponding Tanner graph are governed by certain homogeneous linear equations with integer coefficients. Consequently, we can selectively eliminate cycles from an array code by only retaining those columns from the parity-check matrix of the original code that are indexed by integer sequences that do not contain solutions to the equations governing those cycles. We provide Ramsey-theoretic estimates for the maximum number of columns that can be retained from the original parity-check matrix with the property that the sequence of their indices avoid solutions to various types of cycle-governing equations. This translates to estimates of the rate penalty incurred in shortening a code to eliminate cycles. Simulation results show that for the codes considered, shortening them to increase the girth can lead to significant gains in signal-to-noise ratio (SNR) in the case of communication over an additive white Gaussian noise (AWGN) channel     

Quasi-cyclic LDPC codes for fast encoding

In this correspondence we present a special class of quasi-cyclic low-density parity-check (QC-LDPC) codes, called block-type LDPC (B-LDPC) codes, which have an efficient encoding algorithm due to the simple structure of their parity-check matrices. Since the parity-check matrix of a QC-LDPC code consists of circulant permutation matrices or the zero matrix, the required memory for storing it can be significantly reduced, as compared with randomly constructed LDPC codes. We show that the girth of a QC-LDPC code is upper-bounded by a certain number which is determined by the positions of circulant permutation matrices. The B-LDPC codes are constructed as irregular QC-LDPC codes with parity-check matrices of an almost lower triangular form so that they have an efficient encoding algorithm, good noise threshold, and low error floor. Their encoding complexity is linearly scaled regardless of the size of circulant permutation matrices.     

语音信号频域盲分离中一种频率对准方法

混合语音信号可以使用盲分离频域解法,对观测信号在每一个频点分别进行复值独立分量分析（CICA）算法来解混并得到分离信号,但带来了幅值和次序不定问题（后者又称频率对准）。讨论了频率对准算法中基于DOA估计的方法,并提出了一种基于分离矩阵初始化的频率对准方法,此方法易于实现。通过仿真表明,该方法较好地解决了次序不定问题．对卷积混合语音信号有较好的分离效果。