Improving LDPC and turbo LDPC codes using Collection of Punctured Codes Decoding (CPCD)

In our previous paper [1], a novel CPCD technique has been introduced to significantly improve decoding of LDPC codes over the known sum product algorithm (SPA) decoding. However, results presented in [1] were limited to shorter low density parity check (LDPC) codes and transmission over an addition white Gaussian noise (AWGN) channels using QPSK modulation. In this study, we demonstrate that CPCD can achieve significant gains regardless of the length of the code or the modulation technique used for transmission or the type of the channel including fading channels. In addition, a novel turbo-CPCD technique that follows the principle of turbo LDPC is introduced. It is shown here that CPCD and turbo-CPCD can perform about $0.2-1.5$ dB better than SPA decoding and turbo LDPC codes.     

Genetic optimization of 5G-NR LDPC codes for lowering the error floor of BICM systems

With the wide range of commercial uses of fifth generation (5G), new radio (NR) communication networks, the wireless transmission becomes more efficient, reliable and faster. At the same time, high-quality signal transmission for 5G networks and beyond has also encountered new opportunities and challenges. Channel coding is a key technology to ensure reliable information transmission and service quality. However, the 5G-NR LDPC coded bit-interleaved coded modulation (BICM) sometimes suffers from relatively high error floors, so it can not always guarantee the high-quality and low-delay wireless transmission. In this paper, we propose a further redesign of the 5G-NR LDPC coded BICM based on genetic algorithm (GenAlg). By adjusting the number of the non-zero elements, the corresponding positions and shifting values in base matrix, we optimize the 5G-NR LDPC codes with GenAlg according to the error performances of coded BICM schemes. Simulation results show that the optimized 5G-NR LDPC codes which still support length and rate compatible coding have lower error floors with a little performance loss int the waterfall region compared to the standard 5G-NR LDPC codes with different modulation orders.     

Improving Log-Likelihood Ratio Estimation with Bi-Gaussian Approximation under Multiuser Interference Scenarios

Accurate estimation of channel log-likelihood ratio (LLR) is crucial to the decoding of modern channel codes like turbo, low-density parity-check (LDPC), and polar codes. Under an additive white Gaussian noise (AWGN) channel, the calculation of LLR is relatively straightforward since the closed-form expression for the channel likelihood function can be perfectly known to the receiver. However, it would be much more complicated for heterogeneous networks where the global noise (i.e., noise plus interference) may be dominated by non-Gaussian interference with an unknown distribution. Although the LLR can still be calculated by approximating the distribution of global noise as Gaussian, it will cause performance loss due to the non-Gaussian nature of global noise. To address this problem, we propose to use bi-Gaussian (BG) distribution to approximate the unknown distribution of global noise, for which the two parameters of BG distribution can easily be estimated from the second and fourth moments of the overall received signals without any knowledge of interfering channel state information (CSI) or signaling format information. Simulation results indicate that the proposed BG approximation can effectively improve the word error rate (WER) performance. The gain of BG approximation over Gaussian approximation depends heavily on the interference structure. For the scenario of a single BSPK interferer with a 5 dB interference-to-noise ratio (INR), we observed a gain of about 0.6 dB. The improved LLR estimation can also accelerate the convergence of iterative decoding, thus involving a lower overall decoding complexity. In general, the overall decoding complexity can be reduced by 25 to 50%.     

低密度奇偶校验码在光通信中的性能

低密度奇偶校验码(LDPC)不仅有逼近香农限的良好性能, 而且译码复杂度较低, 结构灵活, 是近年信道编码领域的研究热点, 在光通信系统中有广泛的应用前景。针对非规则Tanner图上构造的低密度奇偶校验长码具有良好的性能, 以及其在光通信系统中的应用, 构造了几种LDPC码, 并采用置信传播(BP)译码, 在加性高期白噪声(AWGN)信道、二相移相键空(BPSK)调制下进行了计算机仿真。根据规则LDPC码和非规则LDPC码的误码率(BER)和FER曲线, 对规则码和非规则LDPC码在编译码方面以及性能方面作了分析和比较, 进而对构造在光通信系统中具有实用价值的LDPC码提出了看法。通过理论分析与仿真结果表明LDPC 码型具有良好的性能, 可以节省硬件开销, 比较适用于光通信系统中, 可作为超强前向纠错码型的候选码。     

基于MMSE的大气激光通信中LDPC码BP译码算法研究

针对大气激光通信中低密度奇偶校验码(LDPC)置信传播(BP)译码算法复杂度高的问题,对几类BP-Based简化译码算法进行了分析,并基于最小均方误差准则(MMSE)对Scaled BP-Based和Offset BP-Based两类改进译码算法的优化设计进行了探讨,得出两类算法的最优校正因子,并给出了数值计算.在不同的湍流强度下,对码长1008的(6,3)比特填充LDPC码进行了仿真实验,结果表明,对于短码长的LDPC码,当译码BER=10-5时,最小和算法(UMP BP-Based)相对于BP算法有0.1～0.15dB的译码性能损失;基于MMSE设计的两类算法相比BP算法大大降低复杂度的同时,译码性能与BP算法相当,甚至优于BP算法,优于UMP BP-Based算法0.075～0.15dB.     

低密度奇偶校验码的性能分析与水下通信验证

在ADSP-BF561上实现了低密度奇偶校验码的编码算法。为解决编码复杂度高的问题,将校验矩阵变换后存入数据空间。为节省存储空间,采用压缩算法,并提出相应的编码算法,没有增加复杂度。对不同码率的低密度奇偶校验码在不同信道中的性能进行仿真分析。将不同码率的低密度奇偶校验码应用于水声通信系统进行浅海试验,结果表明低密度奇偶校验码能提高通信系统的鲁棒性,码率越低性能越好。当解码前符号信噪比在7～8dB时,可达到近似无误码的通信性能。     

基于MMSE的大气激光通信中LDPC码BP译码算法研究

针对大气激光通信中低密度奇偶校验码(LDPC)置信传播(BP)译码算法复杂度高的问题,对几类BP-Based简化译码算法进行了分析,并基于最小均方误差准则(MMSE)对Scaled BP-Based和Offset BP-Based两类改进译码算法的优化设计进行了探讨,得出两类算法的最优校正因子,并给出了数值计算.在不同的湍流强度下,对码长1008的(6,3)比特填充LDPC码进行了仿真实验,结果表明,对于短码长的LDPC码,当译码BER=10^-5时, 最小和算法(UMP BP-Based)相对于BP算法有0.1~0.15 dB的译码性能损失;基于MMSE设计的两类算法相比BP算法大大降低复杂度的同时,译码性能与BP算法相当,甚至优于BP算法,优于UMP BP-Based算法0.075~0.15 dB.     

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.     

基于低密度奇偶校验码的MPPM比特符号映射及系统性能研究

建立了基于低密度奇偶校验(LDPC)码和多脉冲位置调制(MPPM)的无线光通信系统模型,给出了相应系统模型下的解码算法,研究了(m,2)MPPM的比特符号映射方式,提出了用改进的遗传算法(GA)搜索的优化映射方法,最后在大气湍流信道下进行了仿真。仿真结果表明基于LDPC码和MPPM的无线光通信系统性能明显优于未编码的MPPM系统,结合LDPC码和多光束发射技术可以提高系统抗强大气湍流影响的能力;通过GA优化的映射方法在不增加系统复杂性的情况下能进一步提高系统的纠错性能,可以获得更大的编码增益。     

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.     

FPGA-Implemented Fractal Decoder with Forward Error Correction in Short-Reach Optical Interconnects

Forward error correction (FEC) codes combined with high-order modulator formats, i.e., coded modulation (CM), are essential in optical communication networks to achieve highly efficient and reliable communication. The task of providing additional error control in the design of CM systems with high-performance requirements remains urgent. As an additional control of CM systems, we propose to use indivisible error detection codes based on a positional number system. In this work, we evaluated the indivisible code using the average probability method (APM) for the binary symmetric channel (BSC), which has the simplicity, versatility and reliability of the estimate, which is close to reality. The APM allows for evaluation and compares indivisible codes according to parameters of correct transmission, and detectable and undetectable errors. Indivisible codes allow for the end-to-end (E2E) control of the transmission and processing of information in digital systems and design devices with a regular structure and high speed. This study researched a fractal decoder device for additional error control, implemented in field-programmable gate array (FPGA) software with FEC for short-reach optical interconnects with multilevel pulse amplitude (PAM-M) modulated with Gray code mapping. Indivisible codes with natural redundancy require far fewer hardware costs to develop and implement encoding and decoding devices with a sufficiently high error detection efficiency. We achieved a reduction in hardware costs for a fractal decoder by using the fractal property of the indivisible code from 10% to 30% for different n while receiving the reciprocal of the golden ratio.     

基于低密度奇偶校验码的超强前向纠错码设计

光纤中的传输效应(如色散、偏振模色散(PMD)和非线性效应等)会严重影响传输速率和传输距离的进一步提高。因而有必要研究性能更好的新超强前向纠错(Super-FEC) 码型,使其在光通信系统中获得更高的编码增益和更好的纠错性能。简单介绍了低密度奇偶校验(LDPC)码, 然后提出光通信系统中一种基于LDPC码的超强前向纠错(Super-FEC)码型,构造了冗余度为6.68%的新颖LDPC(3969,3720)码, 并给出超强FEC码型的仿真结果。通过与RS(255,239)及BCH(3860,3824)+BCH(2040,1930)进行对比分析, 还分析与探讨了新LDPC码型的编译码电路的设计实现问题。通过理论分析与仿真结果表明这种超强 FEC 码型具有良好的性能, 可以节省硬件开销, 比较适用于光通信系统中, 可作为超强 FEC 码型的候选码。     

Quantum quasi-cyclic low-density parity-check error-correcting codes

Due to the fault of the author(s) of the article entitled “Quantum quasi-cyclic low-density parity-check error-correcting codes”, published inChinese PhysicsB, 2009, Vol. 18, Issue 10, pp 4154--4160, has been found to partly copy from the articlearXiv:quant-ph/0701020v2on the arXiv preprint. So the above article inChinese PhysicsB has been withdrawn from the publication. [2 February 2010]     

Suspicion Distillation Gradient Descent Bit-Flipping Algorithm

We propose a novel variant of the gradient descent bit-flipping (GDBF) algorithm for decoding low-density parity-check (LDPC) codes over the binary symmetric channel. The new bit-flipping rule is based on the reliability information passed from neighboring nodes in the corresponding Tanner graph. The name SuspicionDistillation reflects the main feature of the algorithm—that in every iteration, we assign a level of suspicion to each variable node about its current bit value. The level of suspicion of a variable node is used to decide whether the corresponding bit will be flipped. In addition, in each iteration, we determine the number of satisfied and unsatisfied checks that connect a suspicious node with other suspicious variable nodes. In this way, in the course of iteration, we “distill” such suspicious bits and flip them. The deterministic nature of the proposed algorithm results in a low-complexity implementation, as the bit-flipping rule can be obtained by modifying the original GDBF rule by using basic logic gates, and the modification is not applied in all decoding iterations. Furthermore, we present a more general framework based on deterministic re-initialization of the decoder input. The performance of the resulting algorithm is analyzed for the codes with various code lengths, and significant performance improvements are observed compared to the state-of-the-art hard-decision-decoding algorithms.     

Reverse reconciliation for continuous variable quantum key distribution

An efficient and practical post-processing technique based on reverse reconciliation for continuous variable quantum key distribution is proposed and simulated with low-density parity check (LDPC) codes. MultiLevel Coding/ MultiStage Decoding, which fully utilizes optimization technique such as vector quantization and iterative decoding and the optimal channel coding most close to the Shannon limit, was used to realize efficient reverse reconciliation algorithm. Simulation results showed that the proposed m...     

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.     

Joint physical network coding and LDPC decoding for two way wireless relaying

In this paper, we investigate the joint design of channel and network coding in bi-directional relaying systems and propose a combined low complexity physical network coding and LDPC decoding scheme. For the same LDPC codes employed at both source nodes, we show that the relay can decode the network coded codewords from the superimposed signal received from the BPSK-modulated multiple-access channel. Simulation results show that this novel joint physical network coding and LDPC decoding method outperforms the existing MMSE network coding and LDPC decoding method over the AWGN and complex MAC channel.     

List Decoding of Arıkan’s PAC Codes

Polar coding gives rise to the first explicit family of codes that provably achieve capacity with efficient encoding and decoding for a wide range of channels. However, its performance at short blocklengths under standard successive cancellation decoding is far from optimal. A well-known way to improve the performance of polar codes at short blocklengths is CRC precoding followed by successive-cancellation list decoding. This approach, along with various refinements thereof, has largely remained the state of the art in polar coding since it was introduced in 2011. Recently, Arıkan presented a new polar coding scheme, which he called polarization-adjusted convolutional (PAC) codes. At short blocklengths, such codes offer a dramatic improvement in performance as compared to CRC-aided list decoding of conventional polar codes. PAC codes are based primarily upon the following main ideas: replacing CRC codes with convolutional precoding (under appropriate rate profiling) and replacing list decoding by sequential decoding. One of our primary goals in this paper is to answer the following question: is sequential decoding essential for the superior performance of PAC codes? We show that similar performance can be achieved using list decoding when the list size L is moderately large (say, L⩾128). List decoding has distinct advantages over sequential decoding in certain scenarios, such as low-SNR regimes or situations where the worst-case complexity/latency is the primary constraint. Another objective is to provide some insights into the remarkable performance of PAC codes. We first observe that both sequential decoding and list decoding of PAC codes closely match ML decoding thereof. We then estimate the number of low weight codewords in PAC codes, and use these estimates to approximate the union bound on their performance. These results indicate that PAC codes are superior to both polar codes and Reed–Muller codes. We also consider random time-varying convolutional precoding for PAC codes, and observe that this scheme achieves the same superior performance with constraint length as low as ν=2.     

用于多维数据协调的双边类型LDPC码

在连续变量量子密钥分发(CV-QKD)多维数据协调中,协调效率和密钥传输距离取决于低密度奇偶校验(LDPC)码的纠错性能。在本研究中构造了一种拥有重复累积(RA)码中累积结构的高码率双边类型LDPC码(TET-LDPC),这种双边类型LDPC码在多维数据协调中相比于普通LDPC码可以得到更好的协调性能。经仿真结果可知,在信噪比为1.68 dB时,本文构造的码长为2×10~5的TET-LDPC的协调效率仍然可以达到98.48%,并得到了17.35 kb/s的安全密钥率。