A new coding scheme of QC-LDPC codes for optical transmission systems

Based on Galois Field (GF(q)) multiplicative group, a new coding scheme for Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes is proposed, and the new coding scheme has some advantages such as the simpler construction, the easier implementation encoding, the lower complexity of the encoding and decoding, the more flexible adjustment of the code length as well as the code rate and so forth. Under the condition of considering the characteristics of optical transmission systems, an irregular QC-LDPC (3843,3603) code to be suitable for optical transmission systems is constructed by applying the proposed new coding scheme. The simulation result shows that the net coding gain (NCG) of the irregular QC-LDPC (3843,3603) code is respectively improved 2.14 dB, 1.19 dB, 0.24 dB and 0.14 dB more than those of the classic RS (255,239) code in ITU-T G.975, the LDPC (32640,30592) code in ITU-T G.975.1, the regular SCG-LDPC (3969,3720) code constructed by the Systematically Constructed Gallager (SCG) coding scheme and the regular QC-LDPC (4221,3956) code at the bit error rate (BER) of 10-8. Furthermore, all the five codes have the same code rate of 93.7%. Therefore, the irregular QC-LDPC (3843,3603) code constructed by the proposed new coding scheme has the more excellent error-correction performance and can be better suitable for optical transmission systems.     

Protograph bit-interleaved coded modulation: A bandwidth-efficient design paradigm for 6G wireless communications

Bit-interleaved coded modulation (BICM) has attracted considerable attention from the research community in the past three decades, because it can achieve desirable error performance with relatively low implementation complexity for a large number of communication and storage systems. By exploiting the iterative demapping and decoding (ID), the BICM is able to approach capacity limits of coded modulation over various channels. In recent years, protograph low-density parity-check (PLDPC) codes and their spatially-coupled (SC) variants have emerged to be a pragmatic forward-error-correction (FEC) solution for BICM systems due to their tremendous error-correction capability and simple structures, and found widespread applications such as deep-space communication, satellite communication, wireless communication, optical communication, and data storage. This article offers a comprehensive survey on the state-of-the-art development of PLDPC-BICM and its innovative SC variants over a variety of channel models, e.g., additive white Gaussian noise (AWGN) channels, fading channels, Poisson pulse position modulation (PPM) channels, and flash-memory channels. Of particular interest is code construction, constellation shaping, as well as bit-mapper design, where the receiver is formulated as a serially-concatenated decoding framework consisting of a soft-decision demapper and a belief-propagation decoder. Finally, several promising research directions are discussed, which have not been adequately addressed in the current literature.     

Soft decision decoding of the orthogonal complex MIMO codes for three and four transmit antennas

Orthogonality is a much desired property for MIMO coding. It enables symbol-wise decoding, where the errors in other symbol estimates do not affect the result, thus providing an optimality that is worth pursuing. It also paves the way for low complexity soft decision decoding, which for orthogonal complex MIMO codes is known for two transmit (Tx) antennas, i.e. for the Alamouti code. We propose novel soft decision decoders for the orthogonal complex MIMO codes on three and four Tx antennas and extend the old result of maximal ratio combining (MRC) to cover all orthogonal codes up to four Tx antennas.As a rule, a sophisticated transmission scheme encompasses forward error correction (FEC) coding, and its performance is measured at the FEC decoder instead of at the MIMO decoder. We introduce the receiver structure that delivers the MIMO decoder’s soft decisions to the demodulator, which in turn cranks out the logarithm of likelihood ratio (LLR) of each bit and delivers them to the FEC decoder. This significantly improves the receiver, where a maximum likelihood (ML) MIMO decoder makes hard decisions at a too early stage. Further, the additional gain is achieved with stunningly low complexity.     

Novel memory efficient LDPC decoders for beyond 5G

Beyond-5G wireless networks are expected to gain a excellent trade-off among computational accuracy, latency, and efficient use of available resources. This poses a significant challenge to the channel decoder. In this paper, a novel memory efficient algorithm for decoding Low-Density Parity-Check (LDPC) codes is proposed with a view to reduce the implementation complexity and hardware resources. The algorithm, called Check Node Self-Update (CNSU) algorithm, is based on layered normalized min-sum (LNMS) decoding algorithm while utilizing iteration parallel techniques to integrate both Variable Nodes (VNs) message and A-Posterior Probability(APP) message into the Check Nodes (CNs) message, which eliminates memories of both the VNs message and the APP message as well as updating module of APP message in CNs unit. Based on the proposed CNSU algorithm, design of partially parallel decoder architecture and serial simulations followed by implementation on the Stratix II EP2S180 FPGA are presented. The results show that the proposed algorithm and implementation bring a significant gain in efficient using of available resources, include reducing hardware memory resources and chip area while keeping the benefit of bit-error-rate (BER) performance and speeding up of convergence with LNMS, which are beneficial to apply in Beyond-5G wireless networks.     

基于FPGA的IRIG-B编解码设计与实现

随着系统间时间同步要求的提高,IRIG-B码被越来越多的应用于系统间的时统模块中;针对传统的单片机及专用芯片实现方法已经不能满足产品的可靠性和可移植性的问题,对基于FPGA的IRIG-B编解码设计和实现方法进行了研究;提出了一种将BCD码和二进制码之间相互转换的迭代算法;结合FPGA设计方法对IRIG-B编码和解码方法进行了研究;通过对实验方法进行仿真,结果表明该方法能够正确有效的对时间信息进行IRIG-B格式的解码和编码,并且FPGA内部的实现形式可以大大减少外部芯片及电路的使用,从而大幅提升产品的可靠性和可移植性。     

A novel construction algorithm of the LDPC code for high-speed long-haul optical transmission systems

According to the transmission characteristics of high-speed long-haul optical transmission system, the main construction method of Low-Density Parity-Check (LDPC) code for optical transmission system is presented and a novel construction algorithm of LDPC code is proposed, the theoretical analysis shows that the parity check matrix of the LDPC code constructed by the proposed construction algorithm has no four-girth phenomenon, this is also theoretically proved out. Both the novel LDPC(3969,3720) code with 6.69% redundancy and the novel LDPC(8281,7920) code with 4.56% redundancy for optical transmission systems are constructed by using the presented construction method and proposed construction algorithm. The simulation results show that the net coding gain (NCG) of the two novel LDPC codes at the eighteenth iteration for the BER of 10^?12 are respectively 1.63 dB and 1.49 dB more than that of the RS(255,239) code in ITU-T G.975. Moreover, the decoding of the LDPC code in the hardware can parallel be implemented, so the decoding speed of the two novel LDPC codes are very rapid, the complexities of implementing the two novel LDPC codes, compared with the concatenated codes in ITU-T G.975.1, are relatively lower, furthermore, the hardware overhead and storage space can relatively be saved and the computation complexity can be reduced in implementing the hardware in the future. As a result, the two novel LDPC codes can better be suitable for high-speed long-haul optical transmission systems.     

Design and performance of WH-spread CI/MC-CDMA with iterative interference cancellation receiver

This paper addresses a novel Walsh–Hadamard (WH)-spread multicarrier code division multiple access (MC-CDMA) system which employs carrier interferometry (CI) codes in a multiuser environment. In frequency selective channels, phase characteristics of CI codes ensure better estimates of received WH-spread CI/MC-CDMA signals. Estimation of multiple access interference (MAI) becomes more reliable with time and frequency diversities of CI/MC-CDMA signals with spreading gain diversity of WH codes over multipath channels. Interference cancellation (IC) is done by taking hard and soft estimates of received data bits. Simulation results demonstrate that the proposed multiple access scheme with iterative decoding offer a significant performance gain over WH-spread MC-CDMA and CI/MC-CDMA over multipath channels. We observe that WH-spread CI/MC-CDMA maintains a stable envelope of the transmitted signal as that of CI/MC-CDMA. In an overloaded situation, the proposed multiple access scheme provides a low peak to the average power ratio (PAPR) compared to conventional MC-CDMA for multirate systems which supports simultaneous transmission of high and low data rate users.     

Low-loss belief propagation decoder with Tanner graph in quantum error-correction codes

Quantum error-correction codes are immeasurable resources for quantum computing and quantum communication.However,the existing decoders are generally incapable of checking node duplication of belief propagation(BP)on quantum low-density parity check(QLDPC)codes.Based on the probability theory in the machine learning,mathematical statistics and topological structure,a GF(4)(the Galois field is abbreviated as GF)augmented model BP decoder with Tanner graph is designed.The problem of repeated check nodes can be solved by this decoder.In simulation,when the random perturbation strength p=0.0115-0.0116 and number of attempts N=60-70,the highest decoding efficiency of the augmented model BP decoder is obtained,and the low-loss frame error rate(FER)decreases to 7.1975×10^-5.Hence,we design a novel augmented model decoder to compare the relationship between GF(2)and GF(4)for quantum code[[450,200]]on the depolarization channel.It can be verified that the proposed decoder provides the widely application range,and the decoding performance is better in QLDPC codes.     

水声通信低复杂度最大似然联合均衡译码方法

现有Turbo均衡采用迭代联合均衡译码结构,这一迭代过程在信噪比高于某一门限后才能产生正向的迭代增益,当信道码间干扰较为严重或者采用高阶调制方式时,该信噪比门限较高;同时,现有Turbo均衡的性能还受限于其交织器长度,故当码块长度较短时,其性能并不理想。针对以上问题,提出了一种基于Spinal码的联合均衡译码方法。首先,该方法采用非迭代的最大似然联合均衡译码结构,有效避免了Turbo均衡迭代结构所带来的信噪比门限高问题;其次,该方法采用信息混合能力更强的Spinal码,有助于提高码块长度受限时的误码率性能;最后,该方法利用Spinal码可以有效增加相似信息序列间汉明距离的特点,将联合均衡译码时间复杂度降低为仅随信息序列长度与信道响应长度呈线性增长,解决了本方法难以实际应用于实时水声通信的难题。在抚仙湖湖试中,同样实现速率为3.34kbps数据通信,该方法的误码率优于Turbo均衡方法两个数量级以上。时变水声信道下的仿真以及湖试结果表明,该方法在码长受限的情况下仍在复杂水声信道中表现出更好性能,其所需的最低输入信噪比显著低于现有Turbo均衡方法。      

Performance analysis of a hybrid fiber Bragg grating-based spectral-amplitude-coding/successive interference cancellation for optical CDMA systems

Successive interference cancellation (SIC) scheme is proposed as a new technique that has the potential to reduce the interference and suppress the multiple-access interference (MAI) in spectral-amplitude-coding (SAC) optical-code-division-multiple access (OCDMA) systems. The proposed receiver-based on fiber Bragg gratings (FBGs) techniques. The performance of the proposed system is theoretically analyzed, taking into account various types of noise and interference, including both multiple-access interference (MAI) and receiver noise. Analytical results show that the proposed system offers significant improvement in terms of bit error rate and system capacity (number of users). We have tested our results with both modified prime codes (MPR) and modified quadratic congruence (MQC) codes. In addition, we have compared our proposed system with the corresponding one without cancellation. It has been shown that the proposed scheme gives a substantial increase in capacity.     

MRI梯度预加重模块的分时复用设计

为获得更优的成像质量和更快的成像速度,磁共振成像（MRI）系统的梯度预加重模块需要具有更多的补偿通道和调节参数,常规预加重模块的设计方案使现场可编程门阵列（FPGA）面临巨大的资源消耗.为解决高性能梯度预加重模块的资源消耗大的问题,本文提出了一种基于分时复用技术的梯度预加重实现方案,以常规方案1/44的资源实现了11通道×4组参数的梯度预加重模块.将该模块用于0.35 T MRI系统,测试了补偿前后的涡流曲线和磁共振图像,结果表明该模块有效降低了系统的涡流,减小了磁共振图像中的涡流伪影.     

雾对大气激光通信系统的影响及克服方法

分析了雾产生的原因、相关数学模型及其对大气激光通信系统的影响.为了克服雾对无线光通信链路的影响,将LDPC码作为信道编码应用到大气激光通信系统中,并结合置信传播迭代译码算法和副载波PSK强度调制方案,在有雾的大气信道中进行了仿真.仿真结果表明：LDPC码具有优越的纠错能力,并获得了较大的编码增益,该方案可以满足大气激光通信系统的需要.     

雾对大气激光通信系统的影响及克服方法

分析了雾产生的原因、相关数学模型及其对大气激光通信系统的影响.为了克服雾对无线光通信链路的影响,将LDPC码作为信道编码应用到大气激光通信系统中,并结合置信传播迭代译码算法和副载波PSK强度调制方案,在有雾的大气信道中进行了仿真.仿真结果表明:LDPC码具有优越的纠错能力,并获得了较大的编码增益,该方案可以满足大气激光通信系统的需要.     

Performance analysis of LDPC codes on OOK terahertz wireless channels

Atmospheric absorption, scattering, and scintillation are the major causes to deteriorate the transmission quality of terahertz(THz) wireless communications. An error control coding scheme based on low density parity check(LDPC) codes with soft decision decoding algorithm is proposed to improve the bit-error-rate(BER) performance of an on-off keying(OOK) modulated THz signal through atmospheric channel. The THz wave propagation characteristics and channel model in atmosphere is set up. Numerical simulations validate the great performance of LDPC codes against the atmospheric fading and demonstrate the huge potential in future ultra-high speed beyond Gbps THz communications.     

Multiple decoding for polar-coded chase combining HARQ

The polar-coded hybrid automatic repeat request (HARQ) scheme with chase combining (CC) has very low complexity and is easy to combine with other techniques such as the coded-modulation and space–time coding, etc. However, the CC-HARQ scheme usually suffers from error and throughput performance degradation. A multiple decoding CC-HARQ (MDCC-HARQ) scheme is proposed in this paper by providing extra decoding chances when the joint decoding fails. Specifically, new LLR-sequences are constructed from the received signals, which can be utilized for the extra decoding attempts. Simulation results show that the proposed MDCC-HARQ scheme can achieve better error-performance and higher throughput efficiency, while requires less retransmission when compared with the CC-HARQ scheme.     

Online AL-FEC policy problem on mobile unicast services

Forward error correction (FEC) is a method for error control of data transmission adopted in several mobile multicast standards. FEC is a feedback free error recovery method where the sender introduces redundant data in advance with the source data enabling the recipient to recover from different arbitrary packet losses. Recently, the adoption of FEC error control method has been boosted by the introduction of powerful Application Layer FEC (AL-FEC) codes, e.g. RaptorQ codes. Furthermore, several works have emerged aiming to address the shortcomings of AL-FEC protection application utilizing deterministic or randomized online algorithms to enhance the efficiency of AL-FEC error control method. In this work, since the investigation of AL-FEC application as primary or auxiliary error protection method over mobile multicast environments is a well investigated field but the opportunity of utilizing the AL-FEC over mobile unicast services as the only method for error control replacing common feedback based methods that are now considered to be obsolete, we provide an analysis on the feasibility of AL-FEC protection over unicast delivery utilizing online algorithms in conjunction with AL-FEC codes with exceptional recovery performance.     

On the Performance of Video Resolution,Motion and Dynamism in Transmission Using Near-Capacity Transceiver for Wireless Communication

This article investigates the performance of various sophisticated channel coding and transmission schemes for achieving reliable transmission of a highly compressed video stream. Novel error protection schemes including Non-Convergent Coding (NCC) scheme, Non-Convergent Coding assisted with Differential Space Time Spreading (DSTS) and Sphere Packing (SP) modulation (NCDSTS-SP) scheme and Convergent Coding assisted with DSTS and SP modulation (CDSTS-SP) are analyzed using Bit Error Ratio (BER) and Peak Signal to Noise Ratio (PSNR) performance metrics. Furthermore, error reduction is achieved using sophisticated transceiver comprising SP modulation technique assisted by Differential Space Time Spreading. The performance of the iterative Soft Bit Source Decoding (SBSD) in combination with channel codes is analyzed using various error protection setups by allocating consistent overall bit-rate budget. Additionally, the iterative behavior of SBSD assisted RSC decoder is analyzed with the aid of Extrinsic Information Transfer (EXIT) Chart in order to analyze the achievable turbo cliff of the iterative decoding process. The subjective and objective video quality performance of the proposed error protection schemes is analyzed while employing H.264 advanced video coding and H.265 high efficient video coding standards, while utilizing diverse video sequences having different resolution, motion and dynamism. It was observed that in the presence of noisy channel the low resolution videos outperforms its high resolution counterparts. Furthermore, it was observed that the performance of video sequence with low motion contents and dynamism outperforms relative to video sequence with high motion contents and dynamism. More specifically, it is observed that while utilizing H.265 video coding standard, the Non-Convergent Coding assisted with DSTS and SP modulation scheme with enhanced transmission mechanism results in Eb/N0 gain of 20 dB with reference to the Non-Convergent Coding and transmission mechanism at the objective PSNR value of 42 dB. It is important to mention that both the schemes have employed identical code rate. Furthermore, the Convergent Coding assisted with DSTS and SP modulation mechanism achieved superior performance with reference to the equivalent rate Non-Convergent Coding assisted with DSTS and SP modulation counterpart mechanism, with a performance gain of 16 dB at the objective PSNR grade of 42 dB. Moreover, it is observed that the maximum achievable PSNR gain through H.265 video coding standard is 45 dB, with a PSNR gain of 3 dB with reference to the identical code rate H.264 coding scheme.     

Jointly-check iterative decoding algorithm for quantum sparse graph codes

<正>For quantum sparse graph codes with stabilizer formalism,the unavoidable girth-four cycles in their Tanner graphs greatly degrade the iterative decoding performance with a standard belief-propagation(BP) algorithm.In this paper, we present a jointly-check iterative algorithm suitable for decoding quantum sparse graph codes efficiently.Numerical simulations show that this modified method outperforms the standard BP algorithm with an obvious performance improvement.     

A New Simple Ultrahigh Speed Decoding Algorithm for BCH Code

In order to content with forward error correction (FEC) technology of the high-speed optical communication system, a new simple decoding algorithm for triple-error correcting Bose, Chaudhuri, and Hocquenghem (BCH) code is proposed. Without complicated matrix-operation or division-operation or intricate iterative algorithm, the algorithm is high efficient and high-speed because of its simplicity in structure. The result of hardware emulation confirms that the algorithm is feasible completely. Introduction of the parallel structure increases the speed of coding greatly. The algorithm can be used in the high-speed optical communication system and other fields.     

A New Simple Ultrahigh Speed Decoding Algorithm for BCH Code

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