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.     

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.     

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。     

A new probability decoding scheme based on genetic algorithm for FEC codes in optical transmission systems

Based on the genetic algorithm(GA),a new genetic probability decoding(GPD) scheme for forward error correction(FEC) codes in optical transmission systems is proposed.The GPD scheme can further offset the quantification error of the hard decision by making use of the channel interference probability and statistics information to restore the maximal likelihood transmission code word.The theoretical performance analysis and the simulation result show that the proposed GPD scheme has the advantages of lower decoding complexity,faster decoding speed and better decoding correction-error performance.Therefore,the proposed GPD algorithm is a better practical decoding algorithm.     

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。     

一种适用于光通信系统中的QC-LDPC码的构造

为了满足快速发展的光通信系统不断扩大的需求 ,基于有限域的两个不同本原元提出了一种准循环低密度奇偶校 验(Quasi-Cyclic Low-Density Parity-Check,QC-LDPC)码的构造方法,构造的基矩阵 中不含4环,译码时纠错性能良好。将两 个本原元组合,通过调整基矩阵结构,使构造的码字最小距离增大,从而提升码字的纠错性 能。仿真结果表明:在相同 的仿真环境下,当误比特率(Bit Error Rate,BER)为10－6时 ,构造的码率为93.7%的QC-LDPC(3780540)码的净编码增益(Net Coding Gain,NCG)比同样是利用有限域本原元(Primitive Elements,PE)构造的PE-QC-L DPC(3780540)码,提高了0.38dB;同 时,与适用于光通信中利用有限域中两个不同子群(Sub-Groups,SG)构造的SG-QC-LDPC( 3780540)码和已广泛应用于光通 信的ITU-T G.975.1标准中的LDPC(32 640,30592)码相比,净编码增益 分别有0.2dB和0.72dB的提升。     

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 new construction method of LDPC codes for optical transmission systems

Based on the construction method of systematically constructed Gallager (SCG)(4,k) code,a new improved construction method of low density parity check (LDPC) code is proposed.Compared with the construc...     

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.     

光通信中基于有限域加群的一种QC-LDPC码

针对光通信系统传输特性要求的日益提高,基于有限域GF(q)加群提出了一种构造简单且适合光通信系统的新颖准循环低密度奇偶校验(QC-LDPC)码构造方法,该构造方法可灵活的调整码长、码率且其编译码复杂度低。用此方法构造了适用于光通信系统的规则QC-LDPC(4599,4307)码。仿真结果表明,在BER=10-7时且码率均为93.7%的情况下,所构造的QC-LDPC(4599,4307)码的净编码器增益(NCG)比已广泛应用于光通信系统中的经典RS(255,239)码提高了约2.2dB,比用SCG构造方法构造的SCG-LDPC(3969,3720)码和非规则的QC-LDPC(3843,3603)码的NCG分别提高了约0.47dB和0.25dB,距离香农限约1dB。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。     

一种基于距离图的QC-LDPC构造算法

针对随机法构造的LDPC码结构性差,不易于硬件实现等问题,设计了一种基于距离图的QC-LDPC码构造算法。它有两种实现方式--顺序搜索方式和随机搜索方式,其码长、码率、圈长等参数可以根据实际需要设定,灵活性较好。仿真结果表明:随机搜索方式构造的QC-LDPC码性能明显优于顺序搜索方式,并且与PEG构造的随机码性能相当。与随机构造法相比,文中的搜索算法构造速度更快,并且所构造的码具有准循环特性,易于硬件实现。     

A novel QC-LDPC code based on the finite field multiplicative group for optical communications

A novel construction method of quasi-cyclic low-density parity-check(QC-LDPC) code is proposed based on the finite field multiplicative group,which has easier construction,more flexible code-length code-rate adjustment and lower encoding/decoding complexity.Moreover,a regular QC-LDPC(5334,4962) code is constructed.The simulation results show that the constructed QC-LDPC(5334,4962) code can gain better error correction performance under the condition of the additive white Gaussian noise(AWGN) channel with iterative decoding sum-product algorithm(SPA).At the bit error rate(BER) of 10-6,the net coding gain(NCG) of the constructed QC-LDPC(5334,4962) code is 1.8 dB,0.9 dB and 0.2 dB more than that of the classic RS(255,239) code in ITU-T G.975,the LDPC(32640,30592) code in ITU-T G.975.1 and the SCG-LDPC(3969,3720) code constructed by the random method,respectively.So it is more suitable for optical communication systems.     

A novel decoding algorithm based on the hierarchical reliable strategy for SCG-LDPC codes in optical communications

An effective hierarchical reliable belief propagation （HRBP） decoding algorithm is proposed according to the struc- tural characteristics of systematically constructed Gallager low-density parity-check （SCG-LDPC） codes. The novel decoding algorithm combines the layered iteration with the reliability judgment, and can greatly reduce the number of the variable nodes involved in the subsequent iteration process and accelerate the convergence rate. The result of simulation for SCG-LDPC（3969,3720） code shows that the novel HRBP decoding algorithm can greatly reduce the computing amount at the condition of ensuring the performance compared with the traditional belief propagation （BP） algorithm. The bit error rate （BER） of the HRBP algorithm is considerable at the threshold value of 15, but in the sub- sequent iteration process, the number of the variable nodes for the HRBP algorithm can be reduced by about 70% at the high signal-to-noise ratio （SNR） compared with the BP algorithm. When the threshold value is further increased, the HRBP algorithm will gradually degenerate into the layered-BP algorithm, but at the BER of 10-7 and the maximal iteration number of 30, the net coding gain （NCG） of the HRBP algorithm is 0.2 dB more than that of the BP algo- rithm, and the average iteration times can be reduced by about 40% at the high SNR. Therefore, the novel HRBP de- coding algorithm is more suitable for optical communication systems.     

A novel concatenated code based on the improved SCG-LDPC code for optical transmission systems

Based on the optimization and improvement for the construction method of systematically constructed Gallager (SCG) (4, k) code, a novel SCG low density parity check (SCG-LDPC)(3969, 3720) code to be suitable for optical transmission systems is constructed. The novel SCG-LDPC (6561,6240) code with code rate of 95.1% is constructed by increasing the length of SCG-LDPC (3969,3720) code, and in a way, the code rate of LDPC codes can better meet the high requirements of optical transmission systems. And then the novel concatenated code is constructed by concatenating SCG-LDPC(6561,6240) code and BCH(127,120) code with code rate of 94.5%. The simulation results and analyses show that the net coding gain (NCG) of BCH(127,120)+SCG-LDPC(6561,6240) concatenated code is respectively 2.28 dB and 0.48 dB more than those of the classic RS(255,239) code and SCG-LDPC(6561,6240) code at the bit error rate (BER) of 10 -7 .     

A novel BTC decoding algorithm based on the genetic algorithm in optical communication systems

Combining the advantages of both the genetic algorithm （GA） and the chase decoding algorithm, a novel improved decoding algorithm of the block turbo code （BTC） with lower computation complexity and more rapid decoding speed is proposed in order to meet the developing demands of optical communication systems. Compared with the traditional chase decoding algorithm, the computation complexity can be reduced and the decoding speed can be accelerated by applying the novel algorithm. The simulation results show that the net coding gain （NCG） of the novel BTC decoding algorithm is 1.1 dB more than that of the traditional chase decoding algorithm at the bit error rate （BER） of 10^-6. Therefore, the novel decoding algorithm has better decoding correction-error performance and is suitable for the BTC in optical communication systems.     

利用遗传算法构造QC-LDPC码

考虑到围长(girth)对低密度奇偶校验(LDPC)码的影响,提出了一种利用遗传算法构造大girth的准循环LDPC( QC-LDPC)码的新方法。该方法借助于计算机搜索,多次运用遗传算法,分步提高girth,在得到大girth 的同时,构造出具有准循环结构的LDPC码。分析发现,该构造方法的复杂度与码长成线性关系。仿真结果表明：在误码率( BER)为10-6时,新方法构造的QC-LDPC码比基于欧式几何构造方法、Gallager和Mackay构造法分别获得约0.15 dB、0.5 dB和0.2 dB的净编码增益( NCG),且因具有准循环结构更易于存储和硬件实现。     

A novel segment-shared protection algorithm based on dynamic domain-sequencing scheme for multi-domain optical mesh networks

Survivability has been widely recognized as an important design issue for optical networks. In practice, as the network scale keeps expanding, this design problem becomes more critical. Due to scalability and domain privacy, designing the protection scheme in multi-domain networks is more difficult than that in single domain networks. The path computation element (PCE) is known as an efficient architecture to compute optimal traffic engineering (TE) paths in multi-domain multilayer networks. Based on the PCE architecture, we first propose a new dynamic domain-sequencing scheme that considers the load balance of inter-domain links and then propose an improved segment-shared protection approach called DDSP. It can provide 100% protection ability for multiple failures that each single domain has only one failed link. Finally, the protection based on the optimal dynamic domain-sequencing scheme, called OPT, is designed, to evaluate performance of our algorithm and to provide the good bounding for the dynamic domain-sequencing scheme with limited intra TE information. Simulation evaluation shows that the proposed scheme is effective in multi-domain path protection with more efficient resource utilization, lower blocking probabilities and less inter-domain cost. Furthermore, the performance of it is near to OPT.     

A new construction method of QC-LDPC codes with low error floor based on EETS and Zig-Zag

Aiming at the problem that quasi-cyclic low density parity check (QC-LDPC) codes may have the error floor in the high signal to noise ratio (SNR) region, a new construction method of the QC-LDPC codes with the low error floor is proposed. The basic matrix of the method is based on the progressive edge growth (PEG) algorithm and the improved eliminate elementary trapping sets (EETS) algorithm so as to eliminate the elementary trapping sets in the basic matrix, then the Zig-Zag method is used to construct the cyclic shift matrix which is used to extend the basic matrix in order to construct the parity check matrix. The method not only can improve the error floor in the high SNR region, but also can flexibly design the code length and code rate. The simulation results show that at the bit error rate of 10-6, the PEG-trapping-Zig-Zag (PTZZ)-QC-LDPC(3024,1512) codes with the code rate of 0.5, compared with the PEG-Zig-Zag (PZZ)-QC-LDPC(3024,1512) codes and the PEG-QC-LDPC(3024,1512) codes, can respectively improve the net coding gain of 0.1 dB and 0.16 dB. The difference among the bit error rate performance curves will become better with the increase of the SNR. In addition, the PTZZ-QC-LDPC(3024,1512) codes have no error floor above the SNR of 2.2 dB.