RS码与LDPC码的联合迭代译码

针对RS码与LDPC码的串行级联结构,提出了一种基于自适应置信传播(ABP)的联合迭代译码方法.译码时,LDPC码置信传播译码器输出的软信息作为RS码ABP译码器的输入;经过一定迭代译码后,RS码译码器输出的软信息又作为LDPC译码器的输入.软输入软输出的RS译码器与LDPC译码器之间经过多次信息传递,译码性能有很大提高.码长中等的LDPC码采用这种级联方案,可以有效克服短环的影响,消除错误平层.仿真结果显示:AWGN信道下这种基于ABP的RS码与LDPC码的联合迭代译码方案可以获得约0.8 dB的增益.     

一种低复杂度的LDPC码迭代译码算法

在LDPC码的译码算法中，和积算法性能最优但复杂性较高，最小和算法实现简单但性能与和积算法相差较多。针对这一性能与复杂度的矛盾，带有修正项的最小和算法成为研究的热点问题。文中基于一种性能与和积算法接近的修正最小和算法进行研究，对修正项的修正方式进行了简化，简化后的算法在性能上与和积算法仍非常接近，实现复杂度却比原修正最小和算法有明显的降低。     

一种利用ABP基于可信度迭代的RS码软译码算法

本文研究了自适应置信度传播和分阶统计泽码的级联译码算法(ABP-OSD).然后,我们把ABP-OSD算法和累积对数似然比(ALLR)算法进行结合,提出了一种RS码软译码算法ALLR-ABP-OSD.仿真结果表明,ALLR-ABP-OSD级联算法译码增益有所提高,在RS码译码性能和译码复杂度间取得了较好的折中.     

Iterative Approximate Linear Programming Decoding of LDPC Codes With Linear Complexity

The problem of low complexity linear programming (LP) decoding of low-density parity-check (LDPC) codes is considered. An iterative algorithm, similar to min-sum and belief propagation, for efficient approximate solution of this problem was proposed by Vontobel and Koetter. In this paper, the convergence rate and computational complexity of this algorithm are studied using a scheduling scheme that we propose. In particular, we are interested in obtaining a feasible vector in the LP decoding problem that is close to optimal in the following sense. The distance, normalized by the block length, between the minimum and the objective function value of this approximate solution can be made arbitrarily small. It is shown that such a feasible vector can be obtained with a computational complexity which scales linearly with the block length. Combined with previous results that have shown that the LP decoder can correct some fixed fraction of errors we conclude that this error correction can be achieved with linear computational complexity. This is achieved by first applying the iterative LP decoder that decodes the correct transmitted codeword up to an arbitrarily small fraction of erroneous bits, and then correcting the remaining errors using some standard method. These conclusions are also extended to generalized LDPC codes.      

一种新的终止LDPC迭代译码算法

在传统的卫星广播系统中,信道纠错通常采用BCH码级联LDPC码的方案以达到良好的误码率性能,例如DVB-S2系统。作为内码的LDPC码通常采用迭代译码,且迭代次数较高才能实现比较好的系统性能。借助BCH级联LDPC的结构,文中提出了将BCH检错嵌套进LDPC每一次迭代译码过程中的新的迭代译码结构。仿真结果表明,新算法以较低的BCH码检错运算复杂度换取了LDPC码迭代次数的明显下降,从而极大降低了迭代译码总体复杂度和译码时延,且整体纠错性能与原始LDPC译码后BCH纠错的算法相比基本保持不变。     

Reduced-Complexity Decoding of LDPC Codes

Reduced-Complexity Decoding of LDPC Codes Various log-likelihood-ratio-based belief-propagation (LLR- BP) decoding algorithms and their reduced-complexity derivatives for low-density parity-check (LDPC) codes are presented. Numerically accurate representations of the check-node update computation used in LLR-BP decoding are described. Furthermore, approximate representation of the decoding computations are shown to achieve a reduction in complexity, by simplifying the check-node update or symbol-node update, or both. In particular, two main approaches for simplified check-node updates are presented that are based on the so-called min-sum approximation coupled with either a normalization term or an additive offset term. Density evolution is used to analyze the performance of these decoding algorithms, to determine the optimum values of the key parameters, and to evaluate finite quantization effects. Simulation results show that these reduced-complexity decoding algorithms for LDPC codes achieve a performance very close to that of the BP algorithm. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate scheme from a performance, latency, computational complexity, and memory-requirement perspective.     

Generalized IRA Erasure Correcting Codes for Hybrid Iterative/Maximum Likelihood Decoding

The design of low-density parity-check (LDPC) codes under hybrid iterative / maximum likelihood decoding is addressed for the binary erasure channel (BEC). Specifically, we focus on generalized irregular repeat-accumulate (GeIRA) codes, which offer both efficient encoding and design flexibility. We show that properly designed GeIRA codes tightly approach the performance of an ideal maximum distance separable (MDS) code, even for short block sizes. For example, our (2048,1024) code reaches a codeword error rate of 10^-5 at channel erasure probability isin= 0.450, where an ideal (2048,1024) MDS code would reach the same error rate at isin = 0.453.     

Gradient Projection Decoding of LDPC Codes

A new practical method for decoding low-density parity check (LDPC) codes is presented. The followed approach involves reformulating the parity check equations using nonlinear functions of a specific form, defined over R^rho, where rho denotes the check node degree. By constraining the inputs to these functions in the closed convex subset [0,1]^rho ("box" set) of R^rho, and also by exploiting their form, a multimodal objective function that entails the code constraints is formulated. The gradient projection algorithm is then used for searching for a valid codeword that lies in the vicinity of the channel observation. The computational complexity of the new decoding technique is practically sub-linearly dependent on the code's length, while processing on each variable node can be performed in parallel allowing very low decoding latencies. Simulation results show that convergence is achieved within 10 iterations, although some performance degradations relative to the belief propagation (BP) algorithm are observed     

LDPC卷积码的快速收敛译码

采用串行消息传递策略,文中提出了LDPC卷积码的一种改进的流水线式译码器.分析和仿真结果均表明改进的译码器在不增加单个处理器计算复杂度的前提下,仅通过改变消息传递方式就能够大大加速译码收敛速率,与原译码器相比大约可以节省一半的处理器.     

基于多元LDPC码扩展最小和译码的软信息迭代生成算法

为克服多元LDPC码的扩展最小和(Extended Min-Sum, EMS)译码算法中对数似然比(Log Likelihood Ratio, LLR)生成及排序复杂度过高的问题,该文针对以BPSK为调制方式的编码调制系统,提出一种快速而简单的LLR生成算法。该算法采用一种低复杂度的迭代计算方式,可快速生成并排序LLR,适用于硬件实现的流水线结构,能够加速译码器的译码速度并提高译码器吞吐量。仿真结果表明：所提出算法对译码性能基本没有影响且极大降低LLR计算的复杂度,是一种适用于高速多元LDPC译码器前端实现的候选算法。     

Improved Reliability‐Based Iterative Decoding of LDPC Codes Based on Dynamic Threshold

A serial concatenated decoding algorithm with dynamic threshold is proposed for low‐density parity‐check codes with short and medium code lengths. The proposed approach uses a dynamic threshold to select a decoding result from belief propagation decoding and order statistic decoding, which improves the performance of the decoder at a negligible cost. Simulation results show that, under a high SNR region, the proposed concatenated decoder performs better than a serial concatenated decoder without threshold with an E_b/N₀ gain of above 0.1 dB.     

低密度校验码量化译码研究

介绍了基于置信传播算法的LDPC码和积译码算法，分析其密度进行化特性，对不同消息空间中的量化译码问题进行研究，对采用不同量化方案时LDPC码在AWGN信道下的译码性能进行了仿真。仿真结果表明相对连续译码，中间变量6bit均匀量化会带来约0．4dB左右的损失，而10bit非均匀量化性能明显得到改善。合适的高阶量化译码可以获得接近连续译码的性能。     

Efficient Difference-based Decoding Implementations of LDPC Codes

Efficient implementations of the sum-product algorithm (SPA) for decoding low-density parity-check (LDPC) codes using difference-based messages between bit nodes and check nodes are presented. As for the updates of check nodes, reduced- complexity derivatives are also put forward. As compared with the traditional Log-Likelihood-Ratio(LLR)-based decoding implementations, the proposed method has much lower complexity and latency, while it has no obvious loss of the error performance.     

基于反馈的非均衡X-Z信道量子LDPC译码

针对量子LDPC码,以前期所提出的反馈式和积译码算法(FSPA)为基础,考虑其在非均衡X-Z信道下的译码方法,并分析其相应的性能表现。研究表明在该信道模型下的反馈式策略依然可以借由错误图样对比,译码失败校验子的错误方式,以及信道特征分析,更加有效地调整信息节点上的概率分布,从而大幅提高和积译码器的译码能力。最后,通过实例仿真验证了上述结论。     

Modified Iterative Decoding Algorithm for Polar Code Using Maximum Likelihood Estimation

The key challenges in real time voice communication in long term evolution mobile are reduction in complexity and latency. Efficient encoding and decoding algorithms can cater to these. The implementation of such polar code based efficient algorithms is proposed in this paper. The overall latency of 3.8 ms is needed to process 8 bit block length. The novel sub-matrix near to identity matrix is presented. This resulted into minimization of loops among least reliable bits due to iterated parity check matrix. Look-up table based memory mapping is used in encoder to reduce latency while Euclidian decoding technique is used in decoder. The number of iterations is reduced by 50%. The experimentation is performed with additive white Gaussian noise and QPSK modulation. The proposed modified iterative decoding algorithm requires SNR of 5.5 dB and 192 computations for targeted bit error rate of 10^?4. The second proposed method needs 9 dB, 2 iterations for 384 computations. The penalty paid is quantization error of 0.63% due to restricting computations to fourth order series of hyperbolic function with same 8 bit block length.     

Enhanced Verification-Based Decoding for Packet-Based LDPC Codes

In this letter, an enhanced verification-based decoding algorithm (EVA) for packet level low-density parity-check (LDPC) codes is proposed. Compared with the verification algorithm (VA) in the literature, the proposed algorithm reduces the likelihood of false verification by enhancing the verification condition to achieve a better decoding performance. For example, simulation results in this letter show that EVA reduces frame error rate (FER) by two orders when comparing the VA over binary symmetric channel (BSC), while the increase of the computational load is less than 90%.     

基于大数逻辑可译LDPC码的译码算法研究

本文提出两种基于可靠度的迭代大数逻辑译码算法,从以下两个方面降低译码复杂度:(1)校验节点使用伴随式信息处理,可节省外信息的计算操作;(2)变量节点使用伴随信息进行总信息的投票计数过程.结合非均匀量化技术,接收信号在判决门限附近获得更加精细的处理.此外,本文利用量化参数和列重比例信息对可靠度偏移方向和幅度进行了设计.仿真实验表明,本文提出的算法能够在很低的量化比特(3~4 bits)下有效工作,具有优良的译码性能和快速的收敛速度.     

一种改进的多元LDPC码译码算法

在多元LDPC码的软判决译码算法中,迭代过程中没有使用判决结果和校验和中隐藏的一些信息,在判决结果中隐藏着稳定性信息,校验和中隐藏着变量节点的可靠度信息。从混合译码算法思路出发,借鉴硬判决译码算法中统计校验和的做法和联合迭代检测译码算法中的反馈调整思想,对FFT-BP译码算法进行了改进。改进算法利用迭代过程中的可靠性和稳定度信息,对由变量节点向校验节点传递的消息向量进行调整以使其提供更多正确信息。仿真结果表明,改进的译码算法在没有增加复杂度的前提下,提升了FFT-BP译码算法的性能,在不同参数设置下,性能改进在0.2 d B左右。     

Memory-Efficient and High-Throughput Decoding of Quasi-Cyclic LDPC Codes

We propose turbo-sum-product (TSP) and shuffled-sum-product (SSP) decoding algorithms for quasi-cyclic low-density parity-check codes, which not only achieve faster convergence and better error performance than the sum-product algorithm, but also require less memory in partly parallel decoder architectures. Compared with the turbo decoding algorithm, our TSP algorithm saves the same amount of memory and may achieve a higher decoding throughput. The convergence behaviors of our TSP and SSP algorithms are also compared with those of the SP, turbo, and shuffled algorithms by their extrinsic information transfer (EXIT) charts.     

LDPC编译码技术研究

LDPC码,即低密度奇偶校验码,本质上是一种线性分组码,其译码性能比Turbo码更接近香农限。文中首先介绍了LDPC码的定义及描述;其次对LDPC码快速编码方法进行分析,对可线性编码的LDPC码构造进行探讨;然后对LDPC的译码技术进行研究;最后对LDPC码的应用前景进行讨论。