光通信系统中基于BIBD对QC-LDPC码的研究

基于平衡不完全区组设计(BIBD),深入分析与研究了准循环低密度奇偶校验(QC-LDPC)码的一种新颖构造方法,并通过该构造方法构造了3种同码率不同码长的QC-LDPC码,通过对这3种QC-LDPC码的仿真分析表明,同码率下,码长越长性能越好。同时在BER=10-6时码率均为93.7%的情况下,所构造的BIBD-QC-LDPC(5392,5056)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)码和ITU-T G.975.1中的LDPC(32640,30592)码分别提高了约2.13dB和1.41dB。因而其纠错性能更强,更适用于高速长距离光通信系统。该新颖构造方法简单灵活且编译码更容易实现。     

一种基于修饰技术的改进QC-LDPC码构造方法

基于修饰技术提出了一种改进的准循环低密度奇偶校验(QC-LDPC)码的构造方法.该方法构造的QC-LDPC码具有较低的编码复杂度,其校验矩阵围长至少为6,避免了四环的出现,具有良好的围长特性.仿真分析表明:通过该构造方法构造的码率为93.7％的QC-LDPC(3969,3717)码在降低其编码复杂度的情况下,拥有与其对应的未应用修饰技术的QC-LDPC(3969,3719)码相媲美的纠错性能;并且在相同条件下,QC-LDPC(3969,3717)码的纠错性能要好于利用随机构造方法构造的PEG-LDPC (3969,3720)码,以及ITU-T G.975中已广泛用于光通信系统中的RS(255,239)码和LDPC(32640,30592)码,更适合于光通信系统.     

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。     

光通信系统中一种低复杂度的AP-QC-LDPC码新颖构造方法

提出了一种低复杂度的具有等差数列(AP)特性的准循环低密度奇偶校验(QC-LDPC)码构造方法,该方法结构简单,节省了存储空间,可根据实际需要灵活地改变码长和码率.利用该方法构造出的AP-QC-LDPC(4599,4307)码的校验矩阵的每行元素为等差数列,且公差单调递增,所以该校验矩阵不含有4环.仿真结果表明:在误码率(BER)为10-6时,该AP-QC-LDPC(4599,4307)码比ITU-T G.975中的RS(255,239)码和ITU-T G.975.1中LDPC(32640,30592)码的净编码增益(NCG)分别改善了约2.19和1.48 dB,比基于有限域乘群的eIRA-QC-LDPC(4599,4307)码和QC-LDPC(3780,3540)码的净编码增益分别提高了约0.16和0.2dB.该方法构造的AP-QC-LDPC(4599,4307)码具有更好的纠错性能,能更好地适应光通信系统的需求.     

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。     

光通信中一种基于有限域循环子群的QC-LDPC码构造方法

基于有限域循环子群方法提出了一种结构简单,可以灵活选择码长、码率,并且编译码复杂度低的准循环低密度奇偶校验(QC-LDPC)码构造方法。利用此方法构造出适合光通信系统传输的规则QC-LDPC(5334,4955)码。仿真结果表明该码型利用和积迭代译码算法在加性高斯白噪声信道中取得了很好的性能,比已广泛应用于光通信中的经典RS(255,239)码具有更好的纠错性能。因此所构造的QC-LDPC(5334,4955)码能较好地适用于高速长距离光通信系统。     

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。     

光传输系统中一种新颖的eIRA-QC-LDPC码构造方法

针对光传输系统的特点与要求,基于有限域提出了一种新颖的扩展非规则重复累积准循环低密度奇偶校验码(eIRA-QC-LDPC)构造方法,该构造方法可根据实际需要灵活地调整码长码率,利用此方法构造了一种码率为0.937的novel-eIRA-QC-LDPC(4 599,4 307)码.仿真结果表明:在误码率(BER)为10-7且码率均为0.937的情况下,该novel-eIRA-QC-LDPC (4 599,4 307)码比ITU-T G.975中RS(255,239)码和ITU-T G.975.1中LDPC(32 640,30 592)码的净编码增益(NCG)分别改善了约2.13和1.33 dB,比用SCG构造方法构造的SCG-eIRA-LDPC(3717,3 481)码和基于阵列码构造方法构造的Array-eIRA-QC-LDPC(4 560,4 275)码的净编码增益分别提高了约0.24和0.41 dB,距离香农限约1.07 dB.因而该构造方法所构造的eIRA-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.     

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。     

同类2FSK混合信号中微弱信号提取方法研究

针对光传输系统的特点与要求, 基于有限域提出了一种新颖的扩展非规则重复累积准循环低密度奇偶校验码(eIRA-QC-LDPC)构造方法, 该构造方法可根据实际需要灵活地调整码长码率, 利用此方法构造了一种码率为0.937的novel-eIRA-QC-LDPC(4599,4307)码。仿真结果表明: 在误码率(BER)为10-7且码率均为0.937的情况下, 该novel-eIRA-QC-LDPC(4599,4307)码比ITU-T G.975中RS(255,239)码和ITU-T G.975.1中LDPC(32640,30592)码的净编码增益(NCG)分别改善了约2.13和1.33dB, 比用SCG构造方法构造的SCG-eIRA-LDPC(3717,3481)码和基于阵列码构造方法构造的Array-eIRA-QC-LDPC(4560,4275)码的净编码增益分别提高了约0.24和0.41dB, 距离香农限约1.07dB。因而该构造方法所构造的eIRA-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。     

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 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.     

Construction method of QC-LDPC codes based on multiplicative group of finite field in optical communication

In order to meet the needs of high-speed development of optical communication system, a construction method of quasi-cyclic low-density parity-check (QC-LDPC) codes based on multiplicative group of finite field is proposed. The Tanner graph of parity check matrix of the code constructed by this method has no cycle of length 4, and it can make sure that the obtained code can get a good distance property. Simulation results show that when the bit error rate (BER) is 10-6, in the same simulation environment, the net coding gain (NCG) of the proposed QC-LDPC(3 780, 3 540) code with the code rate of 93.7% in this paper is improved by 2.18 dB and 1.6 dB respectively compared with those of the RS(255, 239) code in ITU-T G.975 and the LDPC(3 2640, 3 0592) code in ITU-T G.975.1. In addition, the NCG of the proposed QC-LDPC(3 780, 3 540) code is respectively 0.2 dB and 0.4 dB higher compared with those of the SG-QC-LDPC(3 780, 3 540) code based on the two different subgroups in finite field and the AS-QC-LDPC(3 780, 3 540) code based on the two arbitrary sets of a finite field. Thus, the proposed QC-LDPC(3 780, 3 540) code in this paper can be well applied in optical communication systems.     

卫星激光通信中基于Fibonacci数列与GCD序列的非规则QC-LDPC码构造方法

为提高卫星激光通信系统的可靠性,节约其硬件资源,提出一种基于斐波那契(Fibonacci)数列与最大公约数(GCD)序列的非规则准循环低密度奇偶校验(Quasi-Cyclic Low-Density Parity-Check, QC-LDPC)码构造方法。该方法通过由Fibonacci数列与GCD序列组合构造的循环移位矩阵扩展原模图基矩阵,从而得到校验矩阵。所构造的校验矩阵围长至少为6且码长码率可灵活选择,需存储元素少,利于硬件实现,较适用于卫星激光通信系统。仿真结果表明,采用该方法构造的非规则QC-LDPC码与相同码率码长的基于完备差集的非规则Type-I QC-LDPC码、基于消除陷阱集的有限长度非规则FL-QC-LDPC码、基于GCD可快速编译的非规则GL-QC-LDPC码以及基于矩阵扩展的非规则RC-LDPC码相比,其净编码增益均有一定提高。