一种新的码率兼容LDPC码打孔方案

该文研究码率兼容LDPC码的打孔问题。Ha等人研究LDPC码打孔时提出的Grouping和Sorting方案使低k-SR节点的数目最大化,它相对于随机打孔有了很大增益,但此方案只保证有一个存活校验节点。该文研究多个存活校验节点的作用,提出MSCN打孔方案最大化打孔节点的存活校验节点数。AWGN信道上的仿真结果显示,低码率时MSCN方案具有比Grouping和Sorting方案更为优越的性能。理论推导及实验结果均表明,码率兼容LDPC码打孔时,多个存活校验节点有益于译码性能的提升。     

一种基于贪婪搜索的码率兼容LDPC码打孔算法

为了提高有限长LDPC码的打孔性能,提出一种码率兼容LDPC码的打孔算法.结合打孔变量点恢复树结构的特点,采用贪婪搜索算法逐级最大化k步可恢复节点的数量,以获得尽可能多的k值较小的k步可恢复节点,从而改善码率兼容系列子码的误码性能.针对随机构造和PEG构造下的LDPC码,验证了本文打孔算法的性能.仿真结果表明,本文方法生成的系列码率兼容子码的误码性能均优于随机打孔方法,特别是当子码的码率较高时,误码性能改善越明显.     

Explicit Codes Achieving List Decoding Capacity: Error-Correction With Optimal Redundancy

In this paper, we present error-correcting codes that achieve the information-theoretically best possible tradeoff between the rate and error-correction radius. Specifically, for every 0 < R < 1 and epsiv < 0, we present an explicit construction of error-correcting codes of rate that can be list decoded in polynomial time up to a fraction (1- R - epsiv) of worst-case errors. At least theoretically, this meets one of the central challenges in algorithmic coding theory. Our codes are simple to describe: they are folded Reed-Solomon codes, which are in fact exactly Reed-Solomon (RS) codes, but viewed as a code over a larger alphabet by careful bundling of codeword symbols. Given the ubiquity of RS codes, this is an appealing feature of our result, and in fact our methods directly yield better decoding algorithms for RS codes when errors occur in phased bursts. The alphabet size of these folded RS codes is polynomial in the block length. We are able to reduce this to a constant (depending on epsiv) using existing ideas concerning ldquolist recoveryrdquo and expander-based codes. Concatenating the folded RS codes with suitable inner codes, we get binary codes that can be efficiently decoded up to twice the radius achieved by the standard GMD decoding.     

一种基于 MDS-卷积码的LDPC码构造方法

近年来,结构化低密度奇偶校验(LDPC)码的构造方法受到了广泛地关注.本文提出了一种利用最大距离分割(MDS)编码构造结构化LDPC码的思路.该思路将基于两个信息符号的RS码构造LDPC码的方法扩展至适用于所有的MDS码.本文以具有MDS特性的卷积码为例详细描述该构造方法的细节,并构造了码长从255比特到4095比特的高码率LDPC码.由于卷积码的MDS定义不同于线性分组码,因此本文给出了一种对卷积码截短的方法及其必要的证明.仿真结果表明,本文构造MDS-Conv-LDPC码的性能优于随机构造的LDPC码.     

Turbo码的删截周期研究

考虑Turbo码的删截周期对汉明重量在删截位置上的分布的影响,得出删截方案的优选对性能的改善程度取决于删截周期的结论,最后通过计算机仿真进行了验证。这一结论对高码率Turbo码的删截方案的优选有重要的指导意义。     

速率无损失的空间耦合LDPC码

空间耦合（spatially coupled）LDPC码为通信系统提供了一种全新的接近容量限的方式,但在耦合过程中需要额外添加校验节点,因此存在一定的码率损失.为了消除码率损失,提出了一种新型的耦合方式,首位置变量节点的边展开方式不变,中间位置的边连接到前一个位置的校验节点并依次向后展开,末位置的边与首位置的边成对称分布,从而得到了一种无需添加额外校验节点,码率无损失的SC-LDPC码变体结构.在AWGN信道中通过外部信息转移（extrinsic information transfer）理论分析及误比特率性能仿真,结果表明：相对于SC-LDPC码的传统结构,本文提出的SC-LDPC码变体结构在链长较短时不仅能避免码率损失,并且具有更优的阈值和译码性能,在未来通信系统中更具优势.     

LDPC码在DSP上的实现

本文概述了LDPC码的编译码原理,重点论述在TI公司的DSP(TMS320C6416)上的(512,256)LDPC编译码器的算法实现,并给出其与(2,1,7)卷积码在AWGN信道条件下的纠错性能对比。对比表明(512,256)LDPC码比(2,1,7)软判决的卷积码在误码率为10-4时可具有1.5dB的编码增益。     

Burst Erasure Correcting LDPC Codes

In this paper low-density parity-check (LDPC) codes are designed for burst erasure channels. Firstly, lower bounds for the maximum length erasure burst that can always be corrected with message-passing decoding are derived as a function of the parity-check matrix properties. We then show how paritycheck matrices for burst erasure correcting LDPC codes can be constructed using superposition, where the burst erasure correcting performance of the resulting codes is derived as a property of the stopping set size of the base matrices and the choice of permutation matrices for the superposition. This result is then used to design both single burst erasure correcting LDPC codes which are also resilient to the presence of random erasures in the received bits and LDPC codes which can correct multiple erasure bursts in the same codeword.     

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.     

High Performance Non-Binary Quasi-Cyclic LDPC Codes on Euclidean Geometries LDPC Codes on Euclidean Geometries

This paper presents algebraic methods for constructing high performance and efficiently encodable non-binary quasi-cyclic LDPC codes based on flats of finite Euclidean geometries and array masking. Codes constructed based on these methods perform very well over the AWGN channel. With iterative decoding using a Fast Fourier Transform based sum-product algorithm, they achieve significantly large coding gains over Reed-Solomon codes of the same lengths and rates decoded with either algebraic hard-decision Berlekamp-Massey algorithm or algebraic soft-decision K?tter-Vardy algorithm. Due to their quasi-cyclic structure, these non-binary LDPC codes on Euclidean geometries can be encoded using simple shiftregisters with linear complexity. Structured non-binary LDPC codes have a great potential to replace Reed-Solomon codes for some applications in either communication or storage systems for combating mixed types of noise and interferences.     

LDPC码及其应用

先在阐述几种LDPC编码的基础上分析了多进制LDPC编码优点;接着介绍作为解释LDPC码和积译码算法的因子图;最后分析了LDPC码的优势以及它在通信领域中应用的可行性。     

基于LDPC码的多中继HARQ系统研究

根据不同中继节点建立的通信信道衰落特性的不同,利用中继节点可增强无线信道空间分集,提高整个链路的传输性能。纠错码的使用可更有效地提高信道传输效率的特点。文中介绍了基于LDPC码的多中继HARQ系统模型,在不降低传输速率的条件下,可更高效地传输数据。利用Matlab仿真了不同中继个数对系统平均误码率、吞吐量以及平均时延产生的不同影响,仿真结果表明,采用该系统模型可降低系统的平均误码率和平均时延,提高了系统的吞吐量。同时在码长较长的情况下,采用LDPC码的多中继HARQ系统性能优于采用Turbo码的多中继HARQ系统性能。     

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.     

LDPC Codes Based on Serially Concatenated Multiple Parity-Check Codes

This letter proposes a new class of serially concatenated codes that can be viewed as Low-Density Parity- Check (LDPC) codes. They are derived from Multiple Serially Concatenated Single Parity-Check (M-SC-SPC) codes, but they use different components, that we call Multiple Parity-Check (MPC) codes. In comparison with M-SC-SPC codes, the new scheme achieves better performance with similar complexity. The proposed codes can represent an alternative to the well-known family of Repeat Accumulate (RA) codes, being based on the same principles.     

Efficient Puncturing Method for Rate-Compatible Low-Density Parity-Check Codes

In this paper, we propose an efficient puncturing method for LDPC codes. The proposed algorithm provides the order of variable nodes for puncturing based on the proposed cost function. The proposed cost function tries to maximize the minimum reliability among those provided from all check nodes. Also, it tries to allocate survived check nodes evenly to all punctured variable nodes. Furthermore, the proposed algorithm prevents the formation of a stopping set from the punctured variable nodes even when the amount of puncturing is quite large. Simulation results show that the proposed punctured LDPC codes perform better than existing punctured LDPC codes.     

基于分段凿孔的极化码级联方案

极化码拥有出色的纠错性能,但编码方式决定了其码长不够灵活,需要通过凿孔构造码长可变的极化码。该文引入矩阵极化率来衡量凿孔对极化码性能的影响,选择矩阵极化率最大的码字作为最佳凿孔模式。对极化码的码字进行分段,有效减小了最佳凿孔模式的搜索运算量。由于各分段的第1个码字都会被凿除,且串行抵消译码过程中主要发生1位错,因此在各段段首级联奇偶校验码作为译码提前终止标志,检测前段码字的译码错误并进行重新译码。对所提方法在串行抵消译码下的性能进行仿真分析,结果表明,相比传统凿孔方法,所提方法在10^–3误码率时能获得约0.7 dB的编码增益,有效提升了凿孔极化码的译码性能。     

一种LDPC码混合迭代译码算法研究

根据LDPC码RRWBF算法和UMP BP-Based算法,提出一种混合迭代译码算法.该算法充分利用硬判决算法具有复杂度低和软判决算法性能好的优点,实现了在误码率性能没有下降的前提下,译码复杂度明显降低的效果,进而使传播时延得到减小.仿真结果表明,经过精心设计的不同迭代次数的MIA算法与性能相当的UMP BP-Based算法相比,译码复杂度降低28.5％.     

Error-Correction Capability of Column-Weight-Three LDPC Codes

In this paper, the error-correction capability of column-weight-three low-density parity-check (LDPC) codes when decoded using the Gallager A algorithm is investigated. It is proved that a necessary condition for a code to correct all error patterns with up to k ges 5 errors is to avoid cycles of length up to 2k in its Tanner graph. As a consequence of this result, it is shown that given any alpha > 0, exist N such that forall n > N, no code in the ensemble of column-weight-three codes can correct all alphan or fewer errors. The results are extended to the bit flipping algorithms.     

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码编码器实现方法

LDPC码是一种系统复杂度低的线性纠错码,其实用化受到了业界的广泛关注。文章概述了LDPC码的基本编码原理,从硬件实现角度概括了LDPC码编码器五种硬件实现方法并对其进行分析,最后指出LDPC码编码器的硬件实现及其发展趋势。