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.     

光传输系统中LDPC码的新颖随机构造方法

分析光传输系统的传输特性与规则LDPC码的随机构造方法之后,提出LDPC码的一种新颖随机构造方法。基于该构造方法构造了一种新颖的码率为93.7%、冗余度为6.69%的规则SCG-LDPC(3969,3720)码,该规则LDPC码在将来的硬件实现中可相对地节省硬件存储空间和减少计算量。仿真分析表明:该新颖的SCG-LDPC(3969,3720)码在BER为10-8时,与同码率同冗余度的ITU-T G.975建议中RS(255,239)码和ITU-T G.975.1建议中LDPC(32640,30592)码相比,其净编码增益(NCG)和距离Shannon限都分别改善了约1.92dB和0.97dB。因而该规则LDPC码的纠错性能更为优越,更适用于光传输系统。     

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。     

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。     

光通信系统中基于等差矩阵的QC-LDPC码

基于等差矩阵的性质特征,提出了一种QC-LDPC(准循环低密度奇偶校验)码的新颖构造方法。该构造方法易于有效编译码,具有良好的围长特性,可有效避免四环,使生成的码字不受短环的干扰,且在硬件实现方面可节省存储空间。仿真结果表明:当误码率达到10-7时,该构造方法造出的高码率QC-LDPC(3780,3542)码与ITU-T G.975中的RS(255,239)码相比,其净编码增益提高了约2.1dB,具有更好的纠错性能;与QC-LDPC(4221,3956)码相比,净编码增益提高了0.35dB。     

一种光通信中基于LDPC码的新颖级联码

基于SCG(4,k)码的构造方法对SCG-LDPC码进行优化改进,构造一种适用于光通信系统的新颖LDPC(3969,3720)码,通过增大其码长,构造码率为95.1%的新颖SCG-LDPC(6561,6240)码,使其码率更符合光通信系统的高码率要求。并用SCG-LDPC(6561,6240)码与码率为94.5%的BCH(127,120)码进行级联,构造出一种新颖的BCH(127,120)+LDPC(6561,6240)级联码。仿真分析表明:在误码率为10-7时,新构造的BCH(127,120)+LDPC(6561,6240)级联码的净编码增益比已广泛应用于光通信系统的经典RS(255,239)码和SCG-LDPC(6561,6240)码分别提高了2.27dB和0.49dB。因而该级联码更适合于光通信系统。     

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。     

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.     

光通信中一种基于有限域的QC-LDPC码构造方法分析

针对光通信系统日益发展的需要,提出了一种的基于有限域准循环低密度奇偶校验(QC-LDPC)码的构造方法.该构造方法简单易行,可以有效避免四环的出现,具有良好的围长特性,同时能够自由地选择码长码率.仿真分析表明:通过该构造方法所构造的码率为93.7％的QC-LDPC(3780,3540)码的纠错性能优于利用随机构造方法所构造的SCG-LDPC (3969,3720)码和已广泛用于ITU-T G.975中的RS(255,239)码和ITU-T G.975.1中的LDPC(32640,30592)码,因而其更适合于光通信系统.     

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 of a new regular LDPC code for optical transmission systems

A novel construction method of the check matrix for the regular low density parity check （LDPC） code is proposed. The novel regular systematically constructed Gallager （SCG）-LDPC（3969,3720） code with the code rate of 93.7% and the redundancy of 6.69% is constructed. The simulation results show that the net coding gain （NCG） and the distance from the Shannon limit of the novel SCG-LDPC（3969,3720） code can respectively be improved by about 1.93 dB and 0.98 dB at the bit error rate （BER） of 10^-8, compared with those of the classic RS（255,239） code in ITU-T G.975 recommendation and the LDPC（32640,30592） code in ITU-T G.975.1 recommendation with the same code rate of 93.7% and the same redundancy of 6.69%. Therefore, the proposed novel regular SCG-LDPC（3969,3720） code has excellent performance, and is more suitable for high-speed long-haul optical transmission systems.     

光通信中基于SCG(4,k)码的一类改进LDPC码构造方法

针对SCG(4,k)码构造方法的分析与研究,提出一种适用于光通信系统中改进的新颖低密度奇偶校验(LDPC)码构造方法.该方法在保留SCG(4,k)构造方法的基础上,采用类似于准循环的构造形式,使生成的码字不受短环干扰,并具有良好的围长特性;并且与改进前的SCG(4,k)码相比,该构造方法具有硬件实现方面节省存储空间和降低计算复杂度等优点.采用该方法构造了码率为93.7％的LDPC(3969,3720)码.仿真结果表明:这种码的净编码增益(NCG)比广泛用于光通信系统中的经典RS(255,239)码提高了1.99 dB.     

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.