PERFORMANCE EVALUATION OF LOW DENSITY PARITY CHECK CODES FOR DIGITAL RADIO MONDIALE (DRM) SYSTEM

In Digital Radio Mondiale (DRM) system, achieving good audio quality becomes a challenge due to its limited band-width of 9 or 10kHz and the very bad fading channels. Therefore, DRM needs highly efficient channel coding schemes. This paper, proposes the schemes which use the Low-Density Parity-Check (LDPC) coded Bit-Interleaved Coded Modulation (BICM) schemes for the implementation of DRM systems. Simulation results show that the proposed system is more efficient than the Rate Compatible Punctured Con volutional (RCPC) coded DRM system on various broadcast channels, and may be recommended as a coding technology for Digital Amplitude Modulation Broadcasting (DAMB) systems of China.

REGULAR LOW-DENSITY PARITY-CHECK CODES BASED ON SHIFTED IDENTITY MATRICES

This paper extends the class of Low-Density Parity-Check (LDPC) codes that can be constructed from shifted identity matrices. To construct regular LDPC codes, a new method is proposed. Two simple inequations are adopted to avoid the short cycles in Tanner graph, which makes the girth of Tanner graphs at least 8. Because their parity-check matrices are made up of circulant matrices, the new codes are quasi-cyclic codes. They perform well with iterative decoding.

THE Q-MATRIX LOW-DENSITY PARITY-CHECK CODES

This paper presents a matrix permuting approach to the construction of Low-Density Parity-Check (LDPC) code. It investigates the structure of the sparse parity-check matrix defined by Gallager. It is discovered that the problem of constructing the sparse parity-check matrix requires an algorithm that is efficient in search environments and also is able to work with constraint satisfaction problem. The definition of Q-matrix is given, and it is found that the queen algorithm enables to search the Q-matrix. With properly permuting Q-matrix as sub-matrix, the sparse parity-check matrix which satisfied constraint condition is created, and the good regular-LDPC code that is called the Q-matrix LDPC code is generated. The result of this paper is significant not only for designing low complexity encoder, improving performance and reducing complexity of iterative decoding arithmetic, but also for building practical system of encodable and decodable LDPC code.

CONSTRUCTION OF NONSYSTEMATIC LOW-DENSITY PARITY-CHECK CODES BASED ON SYMMETRIC BALANCED INCOMPLETE BLOCK DESIGN

This paper studies the nonsystematic Low-Density Parity-Check(LDPC)codes based onSymmetric Balanced Incomplete Block Design(SBIBD).First,it is concluded that the performancedegradation of nonsystematic linear block codes is bounded by the average row weight of generalizedinverses of their generator matrices and code rate.Then a class of nonsystematic LDPC codes con-structed based on SBIBD is presented.Their characteristics include:both generator matrices andparity-check matrices are sparse and cyclic,which are simple to encode and decode;and almost arbi-trary rate codes can be easily constructed,so they are rate-compatible codes.Because there aresparse generalized inverses of generator matrices,the performance of the proposed codes is only0.15dB away from that of the traditional systematic LDPC codes.

Low-Complexity Optimization Algorithm for Irregular Low-Density Parity-Check Codes

A low-complexity algorithm is proposed in this paper in order to optimize irregular low-density parity-check(LDPC)codes.The algorithm proposed can calculate the noise threshold by means of a one-dimensional density evolution and search the optimal degree profiles with fast-convergence differential evolution,so that it has a lower complexity and a faster convergence speed.Simulation results show that the irregular LDPC codes optimized by the presented algorithm can also perform better than Turbo codes at moderate block length even with less computation cost.

DESIGN OF LOW-DENSITY PARITY CHECK CODES FOR MIMO SYSTEMS WITH DOUBLY-ITERATIVE RECEIVERS

In this paper, the Multiple Input Multiple Output (MIMO) doubly-iterative receiver which consists of the Probabilistic Data Association detector (PDA) and Low-Density Parity-Check Code (LDPC) decoder is developed. The receiver performs two iterative decoding loops. In the outer loop, the soft information is exchanged between the PDA detector and the LDPC decoder. In the inner loop, it is exchanged between variable node and check node decoders inside the LDPC decoder. On the light of the Extrinsic Information Transfer (EXIT) chart technique, an LDPC code degree profile optimization algorithm is developed for the doubly-iterative receiver. Simulation results show the doubly-receiver with optimized irregular LDPC code can have a better performance than the one with the regular one.

Low-Density Parity-Check Codes: Research Status and Development Direction

In this paper, we conclude five kinds of methods for construction of the regular low-density parity matrix H and three kinds of methods for the construction of irregular low-density parity-check matrix H. Through the analysis of the code rate and parameters of these eight kinds of structures, we find that the construction of low-density parity-check matrix tends to be more flexible and the parameter variability is enhanced. We propose that the current development cost should be lower with the progress of electronic technology and we need research on more practical Low-Density Parity-Check Codes (LDPC). Combined with the application of the quantum distribution key, we urgently need to explore the research direction of relevant theories and technologies of LDPC codes in other fields of quantum information in the future.

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.

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。

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。

Design of Irregular QC-LDPC Code Based Multi-Level Coded Modulation Scheme for High Speed Optical Communication Systems

In this paper, we focus on the design of irregular QC-LDPC code based multi-level coded modulation(MLCM) scheme by jointly optimizing the component code rate and the degree distribution of the irregular QC-LDPC component code. Firstly, the sub-channel capacities of MLCM systems is analyzed and discussed, based on which the optimal component code rate can be obtained. Secondly, an extrinsic information transfer chart based two-stage searching algorithm is proposed to find the good irregular QC-LDPC code ensembles with optimal component code rates for their corresponding sub-channels. Finally, by constructing the irregular QC-LDPC component codes from the designed ensembles with the aim of possibly enlarging the girth and reducing the number of the shortest cycles, the designed irregular QC-LDPC code based 16QAM and 64QAM MLCM systems can achieve 0.4 dB and 1.2 dB net coding gain, respectively, compared with the recently proposed regular QC-LDPC code based 16QAM and 64QAM MLCM systems.

Design of good QC-LDPC codes without small girth in the p-plane

A construction method based on the p-plane to design high-girth quasi-cyclic low-density parity-check （QC-LDPC） codes is proposed. Firstly the good points in every line of the p-plane can be ascertained through filtering the bad points, because the designed parity-check matrixes using these points have the short cycles in Tanner graph of codes. Then one of the best points from the residual good points of every line in the p-plane will be found, respectively. The optimal point is also singled out according to the bit error rate （BER） performance of the QC-LDPC codes at last. Explicit necessary and sufficient conditions for the QC-LDPC codes to have no short cycles are presented which are in favor of removing the bad points in the p-plane. Since preventing the short cycles also prevents the small stopping sets, the proposed construction method also leads to QC-LDPC codes with a higher stopping distance.

High Robust Broadcasting over DTMB-A with Low-rate LDPC Codes

As the 2nd generation digital terrestrial television broadcasting(DTTB)standard,digital terrestrial/television multimedia broadcasting-advanced(DTMB-A)can provide higher spectrum efficiency and transmission reliability by adopting flexible frame structure and advanced forward error correction coding compared with the 1 st generation DTTB systems.In order to increase the flexibility and robustness of the DTTB network,the frequency reuse scheme of factor one(reuse-1)is proposed,where the same RF channel is used by different stations covering the adjacent service areas.However,it demands a very low carrier-tonoise ratio(C/N)threshold below 0 dB at the DTTB physical layer.In this paper,a robust broadcasting technique is proposed based on DTMB-A with newly designed low-rate low density parity check(LDPC)codes.By adopting quasi-cyclic(QC)Raptor-like structure and progressive lifting method,the high performance low-rate LDPC codes are designed supporting multiple code lengths.Both density-evolution analyses and laboratory measurements demonstrate that DTMB-A with low-rate coding can complete the demodulation reliably with the C/N threshold below0 d B,which is one important necessary condition to support frequency reuse-1 scheme.

Ruling out small stopping sets and small girth in Tanner graph of QC-LDPC code

The existing constructions of quasi-cyclic low-density parity-check （QC-LDPC） codes do not consider the problems of small stopping sets and small girth together in the Tanner graph, while their existences will lead to the bit error rate （BER） performance of QC-LDPC codes being much poorer than that of randomly constructed LDPC codes even decoding failure. To solve the problem, some theorems of the specific chosen parity-check matrix of QC-LDPC codes without small stopping sets and small girth are proposed. A novel construction for QC-LDPC codes with long block lengths is presented by multiplying mmin or the multiple of mmin, which is the minimum order of the identity matrix for the chosen parity-check matrix. The simulation results show that the specific chosen parity-check matrix of QC-LDPC codes can effectively avoid specified stopping sets and small girth and exhibit excellent BER performance than random LDPC codes with the same longer codes length.

基于可靠度差值特征的自适应判决多元LDPC译码算法

利用变量节点符号可靠度在迭代过程中的分布特征,提出了一种基于可靠度差值特征的自适应判决多元低密度奇偶校验(Low Density Parity Check, LDPC)译码算法。整个迭代过程划分为两个阶段,针对不同阶段节点可靠度的差值特征分别采用不同的判决策略:前期阶段,采用传统的基于最大可靠度的判决策略;后期阶段,根据最大、次大可靠度之间的差值特征,设计自适应的码元符号判决策略。仿真结果表明,所提算法在相当的译码复杂度前提下,能获得0.15~0.4 dB的性能增益。同时,对于列重较小的LDPC码,具有更低的译码错误平层。

基于帧交错的LDPC译码器流水结构设计

低密度奇偶校验码(LDPC)的译码器通常采用基于节点置信度更新迭代的算法,这种算法可以并行实现,具有非常高的吞吐量。在此提出了一种具有高硬件利用效率(HUE)的帧交错译码结构,并提供了一种用于层内节点重排序的动态规划方法,解决内存访问冲突问题。与现有的结构相比,该结构可以实现更高的硬件利用效率。

空间耦合低密度奇偶校验码残差滑窗译码算法

针对空间耦合低密度奇偶校验(SC-LDPC)码滑窗译码(SWD)算法中错误传播导致的高误码率问题,该文提出基于动态残差的滑窗译码(RSWD)算法。通过在窗口内计算边信息更新前后的残差值,动态选择可靠度最低(残差值最大)的边信息优先更新,降低边信息无效更新的频率,提高窗内译码收敛速度。仿真结果表明:相比于传统SWD算法,RSWD算法在窗口中各位置的误比特数明显降低,抑制错误传播效果明显;在高信噪比(SNR)区域或者低迭代次数的情况下,RSWD算法的误码率性能优于SWD算法;此外,将动态残差应用到消息复用(MR)和窗口扩展(WE)两种窗译码算法中,亦能得到类似结论,提升窗译码性能。

基于阿贝尔群上的差分集构造LDPC码

本文给出了区组长度为3、4和5的平衡不完全区组设计,将设计的关联矩阵作为校验矩阵,从而构造出3种低密度奇偶校验码(LDPC,low-density parity-check code)。由于这些校验矩阵是准循环矩阵,所以构造的码是拟循环LDPC码(QC-LDPC,quasi-cyclic LDPC)。计算码的相关参数,并针对具体的例子通过与类随机码的译码性能进行分析比较,结果显示,所构造的码具有较好的性能。

Minimum distances of three families of low-density parity-check codes based on finite geometries

Three families of low-density parity-check （LDPC） codes are constructed based on the totally isotropic subspaces of symplectic, unitary, and orthogonal spaces over finite fields, respectively. The minimum distances of the three families of LDPC codes in some special cases are settled.