Dual-CRC polar codes and dual-SCFlip decoding algorithm for cell search in 5G system

Polar codes become the coding scheme for control channels of enhanced mobile broadband (eMBB) scenarios in the fifth generation (5G) communication system due to their excellent decoding performance. For the cell search procedure in 5G system, some common information bits ( CIBs) are transmitted in consecutive synchronization signal blocks ( SSBs). In this paper, a dual-cyclic redundancy check ( dual-CRC) aided encoding scheme is proposed, and the corresponding dual-successive cancellation flip ( dual-SCFlip) algorithm is given to further improve the performance of polar codes in the low signal-to-noise ratio ( SNR) environment. In dual-CRC aided encoding structure, the information bits of polar codes in different transmission blocks add cyclic redundancy check (CRC) sequences respectively according to CIBs and different information bits (DIBs). The structure enlarges the size of CIBs to improve the block error ratio ( BLER) performance of the system. The dual-SCFlip decoder can perform bit flip immediately once CIBs is decoded completely, and then decode DIBs or terminate decoding in advance according to the CRC result, which reduces the delay of decoding and mitigates the error propagation effect. Simulation results show that the dual-CRC aided encoding scheme and dual-SCFlip decoder have significant performance improvement compared to other existing schemes with low SNR.     

A CLASS OF LDPC CODE''''S CONSTRUCTION BASED ON AN ITERATIVE RANDOM METHOD

This letter gives a random construction for Low Density Parity Check (LDPC) codes, which uses an iterative algorithm to avoid short cycles in the Tanner graph. The construction method has great flexible choice in LDPC code's parameters including codelength, code rate, the least girth of the graph, the weight of column and row in the parity check matrix. The method can be applied to the irregular LDPC codes and strict regular LDPC codes. Systemic codes have many applications in digital communication, so this letter proposes a construction of the generator matrix of systemic LDPC codes from the parity check matrix. Simulations show that the method performs well with iterative decoding.     

A CLASS OF LDPC CODE’S CONSTRUCTION BASED ON AN ITERATIVE RANDOM METHOD

This letter gives a random construction for Low Density Parity Check （LDPC） codes, which uses an iterative algorithm to avoid short cycles in the Tanner graph. The construction method has great flexible choice in LDPC code＇s parameters including codelength, code rate, the least girth of the graph, the weight of column and row in the parity check matrix. The method can be applied to the irregular LDPC codes and strict regular LDPC codes. Systemic codes have many applications in digital communication, so this letter proposes a construction of the generator matrix of systemic LDPC codes from the parity check matrix. Simulations show that the method performs well with iterative decoding.     

Quality-Aware Massive Content Delivery in Digital Twin-Enabled Edge Networks

Massive content delivery will become one of the most prominent tasks of future B5G/6G communication. However, various multimedia applications possess huge differences in terms of object oriented(i.e., machine or user) and corresponding quality evaluation metric, which will significantly impact the design of encoding or decoding within content delivery strategy. To get over this dilemma, we firstly integrate the digital twin into the edge networks to accurately and timely capture Quality-of-Decis...     

A Decoding Method Based on RNN for OvTDM

Overlapped X domain multiplexing(Ov XDM) is a promising encoding technique to obtain high spectral efficiency by utilizing Inter-Symbol Interference(ISI). However, the computational complexity of Maximum Likelihood Sequence Detection(MLSD) increases exponentially with the growth of spectral efficiency in Ov XDM, which is unbearable for practical implementations. This paper proposes an Ov TDM decoding method based on Recurrent Neural Network(RNN) to realize fast decoding of Ov TDM system, which has lower decoding complexity than the traditional fast decoding method. The paper derives the mathematical model of the Ov TDM decoder based on RNN and constructs the decoder model. And we compare the performance of the proposed decoding method with the MLSD algorithm and the Fano algorithm. It’s verified that the proposed decoding method exhibits a higher performance than the traditional fast decoding algorithm, especially for the scenarios of a high overlapped multiplexing coefficient.     

Variable non-uniform quantized belief propagation algorithm for LDPC decoding

Non-uniform quantization for messages in Low-Density Parity-Check（LDPC）decoding can reduce implementation complexity and mitigate performance loss.But the distribution of messages varies in the iterative decoding.This letter proposes a variable non-uniform quantized Belief Propagation（BP）algorithm.The BP decoding is analyzed by density evolution with Gaussian approximation.Since the probability density of messages can be well approximated by Gaussian distribution,by the unbiased estimation of variance,the distribution of messages can be tracked during the iteration.Thus the non-uniform quantization scheme can be optimized to minimize the distortion.Simulation results show that the variable non-uniform quantization scheme can achieve better error rate performance and faster decoding convergence than the conventional non-uniform quantization and uniform quantization schemes.     

Program Error Mitigation in MLC NAND Flash Memory with Soft Decision Decoders

Benefiting from strong decoding capabilities,soft-decision decoding has been used to replace hard-decision decoding in various communication systems,and NAND flash memory systems are no exception.However,soft-decision decoding relies heavily on accurate soft information.Owing to the incremental step pulse programming(ISPP),program errors(PEs)in multi-level cell(MLC)NAND flash memory have different characteristics compared to other types of errors,which is very difficult to obtain such accurate soft information.Therefore,the characteristics of the log-likelihood ratio(LLR)of PEs are investigated first in this paper.Accordingly,a PE-aware statistical method is proposed to determine the usage of PE mitigation schemes.In order to reduce the PE estimating workload of the controller,an adaptive blind clipping(ABC)scheme is proposed subsequently to approximate the PEs contaminated LLR with different decoding trials.Finally,simulation results demonstrate that(1)the proposed PE-aware statistical method is effective in practice,and(2)ABC scheme is able to provide satisfactory bit error rate(BER)and frame error rate(FER)performance in a penalty of negligible increasing of decoding latency.     

Bidirectional Viterbi Decoding Algorithm for OvTDM

Overlapped time domain multiplexing(OvTDM)is an innovative encoding scheme that can obtain high spectral efficiency.However,the intentional inter-symbol interference(ISI)caused by OvTDM will make the decoding process more complex.The computational complexity of maximum likelihood sequence detection increases exponentially with the growth of spectral efficiency in OvTDM.As a consequence of high complexity,the decoding effort for a given spectral efficiency may occasionally exceed the physical limitations of the decoder,leading inevitably to buffer overflows and information erasures.In this paper,we propose a bidirectional Viterbi algorithm(BVA)based on the bidirectional sequence decoding for OvTDM.With the BVA,the decoding operation starts simultaneously from the both ends of the corresponding trellis and stops at the middle of trellis.The simulation results show that compared with Viterbi algorithm(VA),the decoding time of BVA can be reduced by about half.And the memory space of two decoders in BVA are about half of that in VA,which means that the BVA has lower memory requirements for decoder.And the decoding performance of BVA is almost the same as VA.     

Improved Reduced Latency Soft-Cancellation Algorithm for Polar Decoding

Soft-cancellation(SCAN) is a soft output iterative algorithm widely used in polar decoding. This algorithm has better decoding performance than reduced latency soft-cancellation(RLSC) algorithm, which can effectively reduce the decoding delay of SCAN algorithm by 50% but has obvious performance loss. A modified reduced latency soft-cancellation(MRLSC) algorithm is presented in the paper. Compared with RLSC algorithm, LLR information storage required in MRLSC algorithm can be reduced by about 50%, and better decoding performance can be achieved with only a small increase in decoding delay. The simulation results show that MRLSC algorithm can achieve a maximum block error rate(BLER) performance gain of about 0.4 dB compared with RLSC algorithm when code length is 2048. At the same time, compared with the performance of several other algorithms under(1024, 512) polar codes, the results show that the throughput of proposed MRLSC algorithm has the advantage at the low and medium signal-to-noise ratio(SNR) and better BLER performance at the high SNR.     

Layered Dynamic Schedulings for BP Decoding of LDPC Codes over GF（q）

A Layered dynamic scheduling （LDS） for Belief-propagation （BP） decoding of LDPC codes over GF（q） is presented, which is derived from the dynamic scheduling for the BP decoding of binary LDPC codes. In order to restrain the LDS from cycling in certain checknodes, a life-index for each check-node is adopted and the optimal value of the life-index is analyzed. Furthermore, in consideration of hardware implementation and decoding latency, a strategy, which allows many more checknodes to be updated in parallel, is introduced. Simulations show that the LDS with life-index speeds up the convergence rate and greatly improves the performance of the BP decoding at medium to high signal-to-noise ratio value, and the algorithm employing the LDS with life-index and the new strategy offers good trade-off between the performance and the decoding latency.     

一种兼容Turbo码的LDPC解码器

提出了一种兼容Turbo码的低密度校验码(LDPC)解码器,它可以将Turbo码完全转化为LDPC码来进行解码,由于采用了校验分裂方法来处理由Turbo码转化而来的LDPC码中所存在的短环,从而使其解码性能优于联合校验置信度传递(JCBP)算法0.8 dB,仅仅比Turbo码专用的BCJR算法损失约为1dB.本文提出的通用解码器,为多系统兼容通信设备的应用提供了一种新的、灵活方便的实现途径.     

基于子迭代次数的LDPC码改进动态调度算法

为了降低低密度奇偶校验(Low Density Parity Check,LDPC)码的译码算法复杂度,提高译码性能,结合基于残余值的动态译码NW-RBP算法和最小和算法,提出了一种基于子迭代次数的改进NW-RBP算法,将此算法称为NW-RBPF算法。该算法在进行残余值计算时利用最小和进行计算,并且根据子迭代过程中每行迭代更新的次数,由仿真得出的收敛因子计算对残余值的补偿值。仿真结果表明,该算法的译码性能相比NW-RBP算法提高了0.05 dB,收敛速度提高了1.5倍,并且其贪婪性降低,是一种适用于LDPC码,且译码性能良好、实现复杂度较低的译码算法。     

基于原型图的低码率LDPC码最小和译码算法改进方案

低密度奇偶校验(LDPC)码的译码硬件实现方案大多采用计算复杂度较低的修正最小和(NMS)算法,然而对于低码率LDPC码,由于校验节点度数低,NMS算法的修正误差较大,导致其译码性能和标准的置信传播(BP)算法相比有较大差异。该文针对基于原图构造的一类低码率LDPC码,提出了在NMS迭代译码中结合震荡抵消(OSC)处理和多系数(MF)修正技术的方案。结合低码率原型图LDPC码行重分布差异较大的特点,MF修正算法可以有效地减少计算误差,从而改善译码性能。另外低码率原型图LDPC码的收敛较慢,而OSC处理则可以较好地抑制正反馈信息,进一步提高NMS算法的性能增益。仿真结果表明,对于此类低码率LDPC码, MF-OSC-NMS算法可以达到接近BP算法的性能。OSC处理和MF修正技术硬件实现简单,与NMS算法相比几乎没有增加计算复杂度,因此MF-OSC-NMS算法是译码算法复杂度和性能之间一个较好的折中处理方案。     

低密度校验码(LDPC码)

低密度校验码（Low Density Parity Check Codes,LDPC codes）是当前编码理论领域研究最热的信道编码之一。本文首先对信道编码研究历程作了简单回顾,然后介绍了LDPC码的发展历程并全面介绍了其相关理论。对LDPC码的和积译码算法（Sum-Product Algorithm,SPA）或置信传播算法（Belief Propagation Algorithm,BPA）、基于二分图的随机构造与代数构造、密度进化理论、高斯近似以及EXIT表分析等相关技术理论的发展和原理进行了详尽的阐述。同时本文还给出近年来LDPC码最新研究成果并给出一些开放性的研究课题。     

A high‐performance belief propagation decoding algorithm for codes with short cycles

The simplicity of decoding is one of the most important characteristics of the low density parity check (LDPC) codes. Belief propagation (BP) decoding algorithm is a well‐known decoding algorithm for LDPC codes. Most LDPC codes with long lengths have short cycles in their Tanner graphs, which reduce the performance of the BP algorithm. In this paper, we present 2 methods to improve the BP decoding algorithm for LDPC codes. In these methods, the calculation of the variable nodes is controlled by using “multiplicative correction factor” and “additive correction factor.” These factors are obtained for 2 separate channels, namely additive white Gaussian noise (AWGN) and binary symmetric channel (BSC), as 2 functions of code and channel parameters. Moreover, we use the BP‐based method in the calculation of the check nodes, which reduces the required resources. Simulation results show the proposed algorithm has better performance and lower decoding error as compared to BP and similar methods like normalized‐BP and offset‐BP algorithms.     

高性能时不变LDPC卷积码构造算法研究

该文基于由QC-LDPC码获得时不变LDPC卷积码的环同构方法,设计了用有限域上元素直接获得时不变LDPC卷积码多项式矩阵的新算法。以MDS卷积码为例,给出了一个具体的构造过程。所提构造算法可确保所获得的时不变LDPC卷积码具有快速编码特性、最大可达编码记忆以及设计码率。基于滑动窗口的BP译码算法在AWGN信道上的仿真结果表明,该码具有较低的误码平台和较好的纠错性能。     

IEEE802.16e标准LDPC译码器设计与实现

LDPC码自在上个世纪90年代被重新发现以来,以其接近香农极限的差错控制性能,以及译码复杂度低、吞吐率高的优点引起了人们的关注,成为继Turbo码之后信道编码界的又一研究热点。利用FPGA设计并实现了一种基于IEEE802.16e标准的LDPC码译码器。该译码器采用偏移最小和（Offset Min-Sum）算法,其偏移因子β取值为0.125,具有接近置信传播（Belief Propagation）算法浮点的性能。译码器在结构上采用了部分并行结构,可以灵活支持标准中定义的所有码率和码长的LDPC码的译码。此外,该译码器还支持对连续输入的数据块进行处理,并具有动态停止迭代功能。硬件综合结果表明,该译码器工作频率为150MHz时,固定15次迭代,最低可达到95Mb/s的译码吞吐率,完全满足802.16e标准的要求。     

Belief propagation decoding of Reed-Solomon codes; a bit-level soft decision decoding algorithm

In this article we propose the application of Belief Propagation (BP) algorithm as a novel bit-level soft decision decoding (SDD) technique for Reed-Solomon (RS) codes. A brief tutorial on Belief Propagation algorithm is presented. A central issue in the application of BP algorithm to decoding RS codes is the construction of a sparse parity check matrix for the binary image of the code. It is demonstrated that Vardy's technique may be applied to find a sparse parity check matrix for RS codes. However, this technique is not applicable to all cases. The BP algorithm is applied to two test codes. In one case, simulation models show that the BP algorithm outperforms the hard decision Euclidean decoding by more than 2 dB of additional coding gain. The results with the second test code are not as promising.     

标准低密度奇偶校验码译码算法中量化结构

DVB-S2标准低密度奇偶校验码(LDPC)译码器在深空通信中面临着低复杂度、高灵活性及普适性方面的迫切需求。通过对LDPC译码算法中量化结构的研究,提出一种动态自适应量化结构的设计方法。该方法在常规均匀硬件量化的基础上,提出了修正化Min-Sum译码算法中的数据信息初始化及迭代译码的动态自适应量化结构,解决了DVB-S2标准LDPC码译码时存在的校验节点运算与变量节点运算之间的复杂度不平衡的问题,并由此提高了译码器的译码性能。实验证明,以DVB-S2标准LDPC码中码长为16 200,码率为1/2的为例,提供动态自适应量化结构与常规的均匀量化结构相比,节省硬件资源为4%。此外,动态自适应量化结构支持动态可配置功能,保证了DVB-S2标准LDPC译码器的灵活性及普适性。     

任意列重大围长QC-LDPC码的确定性构造

针对准循环低密度奇偶校验（Quasi-Cyclic Low-Density Parity-Check,QC-LDPC）码中准循环基矩阵的移位系数确定问题,提出基于等差数列的确定方法.该方法构造的校验矩阵围长为8,列重可任意选取,移位系数由简单的数学表达式确定,编码复杂度与码长呈线性关系,节省了编解码存储空间.研究结果表明,列重和围长是影响码字性能的重要因素.在加性高斯白噪声（Additive White Gauss Noise,AWGN）信道和置信传播（Belief Propagation,BP）译码算法下,该方法构造的码字在短码时可以获得与IEEE 802.11n、802.16e码相一致的性能,在长码时误比特率性能接近DVB-S2码.同时表明该方法对码长和码率参数的设计具有较好的灵活性.