一种新颖的低错误平层LDPC码构造方法

针对低密度奇偶校验(LDPC)码在高信噪比区域可能存在错误平层的缺点,提出了一种低错误平层LDPC码的新构造方法。该方法的基本矩阵由渐进边增长(PEG)算法与近似环额外信息度(ACE)算法相结合,目的是提升基本矩阵中环的连通性;然后将基于分割移位(PS)的循环移位系数矩阵对基本矩阵循环扩展,以此构造出校验矩阵。该方法除了能够改善高信噪比区域的错误平层,还具有码长、码率的任意可设性特点。仿真结果表明,PAP-LDPC(3 600,2 700)码在信噪比为4 dB以后并未出现明显的错误平层。     

一种低差错平底线性复杂度的QC-LDPC码构造方法

本文给出了一种低差错平底QC-LDPC码构造方法.首先,提出了扩展近似下三角阵eALT( extern Approximate Lower Triangular)的全局矩阵构造法,通过对改进后的全局矩阵M进行矩阵置换,生成LDPC码的校验矩阵H以达 到减少小停止集( Stopping Set)数量,降低差错平台(Er...     

基于大衍数列的规则QC-LDPC码构造方法

结合杨辉三角的结构形式,基于大衍数列提出了一种列重为3或4的规则准循环低密度奇偶校验(QC-LDPC)码的新构造方法.该方法构造的校验矩阵围长至少为6,码长可灵活变化,并且可节省存储空间.仿真结果表明:在相同的仿真参数下,当误码率(BER)为10-6时,所构造的列重为3的QC-LDPC(1260,620)码的净编码增益(NCG)比二次函数码改善了1 dB左右;列重为4的QC-LDPC(6056,3028)码相对于WMC-OCS、QC-OCS码分别有0.1 dB和0.2 dB的NCG提升.     

A novel construction method of QC-LDPC codes based on CRT for optical communications

A novel construction method of quasi-cyclic low-density parity-check (QC-LDPC) codes is proposed based on Chinese remainder theory (CRT). The method can not only increase the code length without reducing the girth, but also greatly enhance the code rate, so it is easy to construct a high-rate code. The simulation results show that at the bit error rate (BER) of 10-7, the net coding gain (NCG) of the regular QC-LDPC(4 851, 4 546) code is respectively 2.06 dB, 1.36 dB, 0.53 dB and 0.31 dB more than those of the classic RS(255, 239) code in ITU-T G.975, the LDPC(32 640, 30 592) code in ITU-T G.975.1, the QC-LDPC(3 664, 3 436) code constructed by the improved combining construction method based on CRTand the irregular QC-LDPC(3 843, 3 603) code constructed by the construction method based on the Galois field (GF(q)) multiplicative group. Furthermore, all these five codes have the same code rate of 0.937. Therefore, the regular QC-LDPC(4 851, 4 546) code constructed by the proposed construction method has excellent error-correction performance, and can be more suitable for optical transmission systems.     

光通信系统中基于伽罗华域乘群的QC-LDPC码的一种新颖构造方法

基于Galois域GF(q)乘群,提出了一种构造简单且编码容易实现的新颖准循环低密度奇偶校验(QC-LDPC)码构造方法,可灵活地调整码长、码率,且编译码复杂度低。用本文方法构造了适用于光通信系统的非规则QC-LDPC(3843,3603)码,仿真表明,与已广泛用于光通信系统中的经典RS(255,239)码相比,用本文方法构造的码具有更好的纠错性能,且其性能优于用SCG方法构造的LDPC码和规则的QC-LDPC(4221,3956)码,适合用于高速长距离光通信系统。     

A class of QC-LDPC codes with low encoding complexity and good error performance

We propose a novel approximate lower triangular structure for the parity part of the parity-check matrix of QC-LDPC codes. About half of the non-zero elements in the parity part are set to locate on the upper diagonal while the remaining non-zero elements can be located almost anywhere within the lower triangular area, provided certain rules are observed. Compared with the typical dual-diagonal structure, the proposed structure requires very similar encoding complexity and produces lower error rates over an AWGN channel.     

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 ha...     

A class of irregular LDPC codes with low error floor and low encoding complexity

In this letter, we propose a class of irregular structured low-density parity-check (LDPC) codes with low error floor and low encoding complexity by designing the parity check matrix in a triangular plus dual-diagonal form. The proposed irregular codes clearly lower the error floor and dramatically improve the performance in the waterfall region of error-rate curves. Being characterized by linear encoding complexity, the encoders of the proposed codes attain throughputs over 10 Gbit/s.     

光通信中基于BIBD与循环矩阵分解的QC-LDPC码新颖构造方法

为了满足光通信系统中对纠错码高码率、低误码率(EBR)的要求,基于平衡不完全区组设计(BIBD)和循环矩阵分解,提出一种构造简单的新颖准循环低密度奇偶校验(QC-LDPC)码构造方法,并构造了适用于光通信系统的规则BIBDdes-QC-LDPC(6736,6316)码。仿真结果表明,在BER=10-6时其码率均为93.7%的情况下,所构造的BIBDdes-QC-LDPC(6736,6316)码的净编码增益(NCG)比已广泛应用于光通信系统中的经典RS(255,239)码改善了约2.2dB,并且比只基于BIBD所构造的同码率同码长的规则BIBD-QC-LDPC(6736,6315)和基于伽罗华域(GF)乘群所构造的同码率的非规则QC-LDPC(3843,3603)码都分别改善了约0.2dB。因而,运用本文方法构造的QC-LDPC码型的纠错性能更强,更适用于高速长距离光通信系统。并且,本文方法还具有BIBD构造方法的优点,可灵活地调整码率码长。     

光通信中基于伽罗华域的QC-LDPC码构造方法

为了满足光通信系统对纠错码高码率、低误码率的要求,基于伽罗华域中域的特征提出了一种结构简单、易于编码并且可以有效避免四环的 QC-LDPC(准循环低密度奇偶校验)码的新构造方法。并运用该方法构造了适用于光通信系统的 FC-QC-LDPC(基于域特征的 QC-LDPC)(3969,3729)码。仿真结果表明,在误码率=10-7时,所构造的码率为0.937的 FC-QC-LDPC(3969,3729)码的 NCG (净编码增益)比 QC-LDPC(4288,4020)码提高了约0.15 dB,比 Linshu-QC-LDPC(3780,3542)码和经典的 RS(255,239)码的 NCG分别提高了约0.35和2.1 dB。此外,所构造的码的性能与 Mackay码的性能相当。因而其纠错性能更强,更适用于高速长距离光通信系统。     

基于改进2-DGRS码的QC-LDPC码高效构造

利用GRS(generalized reed-solomon)码的生成多项式提出了基于改进的2-D GRS(two-dimensional GRS)码设计和构造QC-LDPC(quasi-cyclic low density parity-check)码的方法,使所构造的码具有较好的译码性能。同时在码的构造过程中,考虑到了准双对角线结构和合适的度分布。不同码率的LDPC码用于和新设计的QC-LDPC码进行测试和比较。实验结果表明,所提出的码构造方法可加快LDPC码校验矩阵的构造,同时基于所提出方法构造的QC-LDPC码可提高译码性能,并降低编码复杂度。     

一种高速长距离光通信系统中QC-LDPC码的构造方法

提出了一种新的准循环低密度奇偶校验(QC-LDPC)码的构造方法,给出了用该方法构造无环四QC-LDPC码的充分条件。并针对光通信系统的传输特点,用此方法构造了适用于高速长距离光通信系统的QC-LDPC(4 221,3 956)码。仿真结果分析表明:在码率为93.7%、误码率BER为10-6时,与广泛用于光通信系统中的经典RS(255,239)码相比,其净编码增益(NCG)提高了约1.8dB;比SCG-LDPC(3 969,3 720)码的NCG提高了约0.2dB,距离香农极限约1.4dB,且远低于PEG-LDPC(4 221,3 956)码的错误平层,这正满足光通信系统中低错误平层的要求。     

围长为8的QC-LDPC码的显式构造及其在CRT方法中的应用

对于任意码长PL(P≥3L2/4+L 1),利用完全确定的方式构造出一类围长为8的(4,L)QC-LDPC码。将这类码作为分量码,结合中国剩余定理(CRT)构造出一类围长至少为8且码长非常灵活的合成QC-LDPC码。在1/2码率和中等码长条件下的仿真结果表明,这种合成码在AWGN信道下具有优异的性能。     

A novel construction scheme of QC-LDPC codes based on the RU algorithm for optical transmission systems

A novel lower-complexity construction scheme of quasi-cyclic low-density parity-check (QC-LDPC) codes for optical transmission systems is proposed based on the structure of the parity-check matrix for the Richardson-Urbanke (RU) algorithm. Furthermore, a novel irregular QC-LDPC(4 288, 4 020) code with high code-rate of 0.937 is constructed by this novel construction scheme. The simulation analyses show that the net coding gain (NCG) of the novel irregular QC-LDPC(4 288,4 020) code is respectively 2.08 dB, 1.25 dB and 0.29 dB more than those of the classic RS(255, 239) code, the LDPC(32 640, 30 592) code and the irregular QC-LDPC(3 843, 3 603) code at the bit error rate (BER) of 10-6. The irregular QC-LDPC(4 288, 4 020) code has the lower encoding/decoding complexity compared with the LDPC(32 640, 30 592) code and the irregular QC-LDPC(3 843, 3 603) code. The proposed novel QC-LDPC(4 288, 4 020) code can be more suitable for the increasing development requirements of high-speed optical transmission systems.     

A novel construction method of QC-LDPC codes based on the subgroup of the finite field multiplicative group for optical transmission systems

According to the requirements of the increasing development for optical transmission systems, a novel construction method of quasi-cyclic low-density parity-check (QC-LDPC) codes based on the subgroup of the finite field multiplicative group is proposed. Furthermore, this construction method can effectively avoid the girth-4 phenomena and has the advantages such as simpler construction, easier implementation, lower encoding/decoding complexity, better girth properties and more flexible adjustment for the code length and code rate. The simulation results show that the error correction performance of the QC-LDPC(3 780,3 540) code with the code rate of 93.7% constructed by this proposed method is excellent, its net coding gain is respectively 0.3 dB, 0.55 dB, 1.4 dB and 1.98 dB higher than those of the QC-LDPC(5 334,4 962) code constructed by the method based on the inverse element characteristics in the finite field multiplicative group, the SCG-LDPC(3 969,3 720) code constructed by the systematically constructed Gallager (SCG) random construction method, the LDPC(32 640,30 592) code in ITU-T G.975.1 and the classic RS(255,239) code which is widely used in optical transmission systems in ITU-T G.975 at the bit error rate (BER) of 10^-7. Therefore, the constructed QC-LDPC(3 780,3 540) code is more suitable for optical transmission systems.     

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。     

Flexible construction of irregular partitioned permutation LDPC codes with low, error floors

Irregular partitioned permutation (IPP) low-density parity-check (LDPC) codes have been recently introduced to facilitate hardware implementation of belief propagation (BP) decoders. In this letter, we present a new method to construct IPP LDPC codes with great flexibility in the selection of code parameters. Meanwhile, small stopping sets are avoided in the code construction, thus good error floor performance can be achieved.     

基于中国剩余定理和贪婪算法扩展的QC-LDPC码

在缩短阵列码的基础上运用中国剩余定理(CRT)和贪婪算法提出了一种新颖的大围长、码长更加灵活的QC-LDPC构造方法,且所构造的码字的校验矩阵采用楼梯矩阵循环置换而成。与传统CRT构造方法相比,只需已知一个分量码——缩短阵列码,同时新构造QC-LDPC码码长与码率选择比较灵活,围长更大,如果围长一样,则使最短环数量尽可能地少。仿真分析表明:在误码率为10-6时,在相同码率和码长的条件下,利用所提出的构造方法所构造的girth-8(4,k)QC-LDPC码在加性高斯白噪声(AWGN)和瑞利衰落信道中分别与缩短阵列码相比可获得约1.2 d B和2.0 d B的净编码增益,与CRT码相比分别改善了0.3 d B和0.7 d B的净编码增益,且性能与Gallager随机码性能相似但编码复杂度大大降低。     

基于EETS与GC的非规则QC-LDPC码低错误平层构造方法

针对准循环低密度奇偶校验(QC-LDPC)码在高信噪比区域可能出现的错误平层现象,提出了一种基于消除基本陷阱集(Eliminating Elementary Trapping Sets, EETS)和围长约束(Girth Constraints, GC)的非规则QC-LDPC码构造方法。该方法通过巧妙选取度分布,利用基本陷阱集搜索和围长约束改进渐进边增长(Progressive Edge Growth, PEG)算法构造基矩阵,然后通过等差(Arithmetic Progression, AP)序列扩展得到所需的校验矩阵。该方法仅需对简单环形式的ETS进行搜索和消除,就能确保构造的基矩阵中不存在设置范围内的绝大多数ETS,从而降低错误平层现象,且该方法计算复杂度相对较低,可灵活设计码长码率。仿真结果表明,由所提出构造方法构造的非规则QC-LDPC码比其他五种QC-LDPC码的纠错性能更为优越,且没有明显的错误平层现象。     

A construction of codes with exponential error bounds on arbitrarydiscrete memoryless channels

This correspondence proposes an explicit construction of codes achieving capacity for arbitrary discrete memoryless channels. The proposed code is obtained by concatenating variable inner codes and an algebraic geometry code. Further, we clarify that the proposed code achieves the error exponent obtained by Forney for concatenated codes