Study on New Concatenated Code in WDM Optical Transmission Systems

A new concatenated code of RS（255,239）＋BCH（2 040,1 930） code to he suitable for WDM optical transmission systems is proposed. The simulation resuhs show that this new concatenated code. compared with the RS（255,239）4-CSOC（k0/n0=6/7, J= 8） code in ITU-TG. 75.1, has a lower redundancy and better error-correction performance, furthermore, its net coding gain（NCG） is respectively 0. 46 dB, 0.43 dB morethanthatofRS（255,239）＋CSOC（k0/n0= 6/7, J= 8） code and BCH（3860,3824）＋BCH （2 040,1 930） code in ITU TG. 75. 1 at the third iteration for the bit error rate（BER） of 10^-12. Therefore, the new super forward error correction（Super-FEC） concatenated code can be better used in ultra long-haul, ultra large-capacity and ultra high-speed WDM optical communication systems.     

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。     

前向纠错技术在100Gb/s系统中的研究

通过对软判决、低密度奇偶校验码(LDPC)编码进行了研究,构造了更高编码增益的LDPC与里德-索罗门码(RS)级联码.仿真结果表明,RS和软判决LDPC级联的编码方式,能够在RS(255,239)的基础之上提高4.5dB的编码增益.     

光通信系统中一种新颖FEC码的仿真分析

基于分组Turbo码（BTC）提出光通信系统中一种新颖前向纠错（FEC）码型,即RS（63,60）×RS（63,60）码。仿真表明,在误码率为10-12时,迭代8次的该BTC与ITU-T G.975.1中迭代3次的RS（255,239）＋CSOC（k0/n0=6/7,J=8）相比,其净编码增益要相应增加0.34dB。分析表明该BTC具有分量码短、编/译码速度快的特点,不仅减小了软/硬件实现的复杂度,而且减小了编/译码带来的时延。因而该新BTC能较好地适用于光通信系统。     

光通信系统中交织型级联码性能的研究

对光通信系统中单级型级联码和交织型级联码的纠错性能进行理论研究与仿真分析后表明:交织型级联码的纠错性能与单级型级联码基本相当,与经典的RS(255,239)码型相比,其净编码增益(NCG)大得多,纠错性能有很大的提升;交织型级联码的冗余度比单级型级联码要低得多,并且还具有比单级型级联码更强的纠突发差错能力。因而交织型级联码更适合光通信系统的实际应用要求。     

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 .     

迭代译码的级联Reed-Solomon乘积码与卷积码

该文提出用Reed Solomon(RS)乘积码作为外码,卷积码作为内码的级联码方案并且内外码间用Congruential向量生成的交织图案对RS码符号进行重排列。对此级联码采用的迭代译码基于成员码的软译码算法。当迭代次数达到最大后,通过计算RS码的校正子,提出一种纠正残余错误的方法,进一步提高了系统的误比特性能。仿真结果表明,在AWGN信道中与迭代译码的级联RS/卷积码相比,当误比特率为1e-5时,新系统的编码增益大约有0.4 dB。     

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。     

Reed-Solomon codes for correcting phased error bursts

A code structure is introduced that represents a Reed-Solomon (RS) code in two-dimensional format. Based on this structure, a novel approach to multiple error burst correction using RS codes is proposed. For a model of phased error bursts, where each burst can affect one of the columns in a two-dimensional transmitted word, it is shown that the bursts can be corrected using a known multisequence shift-register synthesis algorithm. It is further shown that the resulting codes posses nearly optimal burst correction capability, under certain probability of decoding failure. Finally, low-complexity systematic encoding and syndrome computation algorithms for these codes are discussed. The proposed scheme may also find use in decoding of different coding schemes based on RS codes, such as product or concatenated codes.     

光通信系统中级联码性能分析

通过对光通信系统的发展趋势和级联码的理论进行分析后,对光通信系统中传统级联码、并行型级联码和交织型级联码三种级联码的性能进行了深入研究。通过理论分析与仿真结果表明:传统级联码冗余度过大,并行型级联码的译码实现过于复杂,而交织型级联码是一种纠错性能优良、冗余度适中、易于实现的码型,更适用于光通信系统。     

Forward error correction concatenated code in DWDM systems

The three concatenated coding schemes of the inner-outer type, the parallel type and the consecutive type to improve the current forward error correction (FEC)coding technologies are proposed for dense wavelengthdivision multiplexing (DWDM) systems, after introducing the development trend of DWDM optical communication systems. The concatenated code is theoretically analyzed.The theoretical analyses and simulation results show that inner-outer concatenated code has a greater redundancy and the decoding of parallel concatenated code is too complex. However, consecutive concatenated code is superior coding scheme with advantages such as better error correction performance, moderate redundancy and easy implementation, therefore it could be better used in high-speed and long-haul DWDM systems.     

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。     

非二进制Turbo级联码的性能分析

该文在分析了非二进制Turbo码的译码算法的基础上,提出了非二进制Turbo码和具有良好纠突发错误的RS码级联的非二进制Turbo级联码系统模型。该系统采用缩短的RS码(204, 188)作为外码,非二进制Turbo码作为内码的串行级联方式,内码和外码之间用深度为12的交织器隔开,译码时, 非二进制Turbo码分别采用Symbol-by-Symbol Log-MAP和SOVA算法。仿真结果显示,与二进制Turbo级联码系统相比,该系统具有误码率低,延时时间短,频带利用率高等优点。     

低时延RS-CC级联码的设计与实现

为提高手持无线电台的纠错和时延特性,考虑设计一种短码长RS-CC级联码.通过对Reed-Solomon码缩短和截断以及对卷积码删余,提出了一种低时延的级联码设计方案,并进行性能分析和软硬件实现.结果表明,在高斯信道下,当Eb/No达到4.2 dB时,能够实现10-4的误码率性能.设计的RS-CC级联码码长较短,编解码固有时延低,译码速度提升30％,适合低时延应用.     

GPON中高速并行RS编码器的实现

RS码是一种纠错能力很强的线性分组码,可大幅提高通信系统性能。针对吉比特无源光网络,设计并实现了32位并行RS（255,239）编码器。编写VerilogHDL代码,利用QuartusII软件验证功能的正确性。结果表明该编码器运行速度快,占用资源少,满足GPON系统高速数据传输的要求。     

Performance of RS coded M-ary modulation with and without symbol overlapping

In this paper, we present analytical bit error probability results for M-ary modulation concatenated with Reed Solomon (RS) codes. The analysis of bit error probability is nontrivial as the number of bits per symbol for the RS codes may not be an integer multiple of the number of bits per symbol for a modulation symbol. We propose a Markov chain technique which allows analytical evaluation of the bit error probability for such cases. The performance of RS coding with coherent biorthogonal, coherent/non-coherent orthogonal modulation over an additive white Gaussian noise (AWGN) channel is evaluated. Simulation of the bit error probability of RS code concatenated with a Nordstrom Robinson (NR) code as an inner code is performed and compared with the case of biorthogonal modulation. From the results, we notice that a stronger inner code gives better bit error probability. In addition, the throughput of the coded system with biorthogonal modulation over an AWGN channel is discussed. For a Rayleigh flat fading and block fading channel, we analyze the bit error probability of RS codes concatenated with biorthogonal modulation. From the result, we notice that a stronger outer code gives a better bit error probability for the case of Rayleigh flat fading channel.     

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。     

基于Logistic混沌序列的错误图样对纠错码的影响

为了在“比特级”层面对纠错码进行更深入的研究,提出了一种服从Logistic混沌序列的错误图样分布模型。通过将混沌序列映射成二进制序列,并采用一定的方法使序列中“1”的数目可控,以此来生成错误图样。将卷积码、RS码以及RS+卷积级联码作为研究对象,以随机错误为参照,分别研究了该错误图样下三者的译码性能。仿真结果表明,基于Logistic混沌序列的错误图样对卷积码和级联码的影响要大于随机错误图样,而随机错误图样对RS码的影响更大。     

Cyclic unequal error protection codes constructed from cyclic codesof composite length

The unequal error correction capabilities of binary cyclic codes of composite length are investigated. Under certain conditions, direct sums of concatenated codes have unequal error correction capabilities. By a modified Hartmann and Tzeng (1973) algorithm, it is shown that a binary cyclic code of composite length is equivalent to the direct sum of concatenated codes. With this, some binary cyclic unequal error protection (UEP) codes are constructed. Finally, the authors present a class of two-level UEP cyclic direct-sum codes which provide error correction capabilities higher than those guaranteed by the Blokh-Zyablov (1974) constructions