Upper Bound on Error Exponent of Regular LDPC Codes Transmitted Over the BEC

The error performance of the ensemble of typical low-definition parity-check (LDPC ) codes transmitted over the binary erasure channel (BEC) is analyzed. In the past, lower bounds on the error exponents were derived. In this paper, a probabilistic upper bound on this error exponent is derived. This bound holds with some confidence level.      

纠删信道中LDPC码EXIT曲线匹配设计

基于单栓码和重复码EXIT图面积特性的分析,介绍了在二元纠删信道中,采用EXIT曲线匹配设计LDPC码度分布序列的最佳性:当内外码的EXIT曲线完全匹配时,所设计的度分布序列对应的速率能够达到信道容量;而当内外码EXIT曲线之间有间隔时,所设计的度分布序列对应的速率严格小于信道容量,并且间隔面积越大,所损失的速率越大.     

LDPC Codes Over Rings for PSK Modulation

This paper describes the design and analysis of low-density parity-check (LDPC) codes over rings and shows how these codes, when mapped onto appropriate signal constellations, can be used to effect bandwidth-efficient modulation. Specifically, LDPC codes are constructed over the integer rings$BBZ_m$and$BBG_m^2$and mapped onto phase-shift keying (PSK)-type signal sets to yield geometrically uniform signal space codes. This paper identifies and addresses the design issues that affect code performance. Examples of codes over$BBZ_8$and$BBG_64$mapped onto$8$-ary and$64$-ary signal sets at a spectral efficiency of 1.5 and 2.0 bits per second per hertz (b/s/Hz) illustrate the approach; simulation of these codes over the additive white Gaussian noise (AWGN) channel demonstrates that this approach is a good alternative to bandwidth-efficient techniques based on binary LDPC codes—e.g., bit-interleaved coded modulation.     

FFT-Based BP Decoding of General LDPC Codes Over Abelian Groups

We introduce a wide class of low-density parity-check (LDPC) codes, large enough to include LDPC codes over finite fields, rings, or groups, as well as some nonlinear codes. A belief-propagation decoding procedure with the same complexity as for the decoding of LDPC codes over finite fields is also presented. Moreover, an encoding procedure is developed     

The Universal Operation of LDPC Codes Over Scalar Fading Channels

Root and Varaiya proved the existence of a code that can communicate reliably over any linear Gaussian channel for which the channel mutual information level exceeds the transmitted rate. This paper provides several examples of scalar (single-input single-output) fading channels and shows that on these channels the performance of low-density parity-check (LDPC) codes lies in close proximity to the performance limits identified by Root and Varaiya. Specifically, we consider periodic fading channels and partial-band jamming (PBJ) channels. A special case of periodic fading is the variation of signal-to-noise ratio across orthogonal frequency division modulation subchannels. The robustness of LDPC codes to periodic fading and PBJ across parameterizations of these different channels is demonstrated through the consistency of the required mutual information to provide a specified bit error rate. For the periodic fading case, the Gaussian approximation to density evolution has been adapted such that asymptotic threshold measures can be compared to simulated code performance in various periodic fading scenarios     

An Improved Sphere-Packing Bound for Finite-Length Codes Over Symmetric Memoryless Channels

This paper derives an improved sphere-packing (ISP) bound for finite-length error-correcting codes whose transmission takes place over symmetric memoryless channels, and the codes are decoded with an arbitrary list decoder. We first review classical results, i.e., the 1959 sphere-packing (SP59) bound of Shannon for the Gaussian channel, and the 1967 sphere-packing (SP67) bound of Shannon et al. for discrete memoryless channels. An improvement on the SP67 bound, as suggested by Valembois and Fossorier, is also discussed. These concepts are used for the derivation of a new lower bound on the error probability of list decoding (referred to as the ISP bound) which is uniformly tighter than the SP67 bound and its improved version. The ISP bound is applicable to symmetric memoryless channels, and some of its applications are presented. Its tightness under maximum-likelihood (ML) decoding is studied by comparing the ISP bound to previously reported upper and lower bounds on the ML decoding error probability, and also to computer simulations of iteratively decoded turbo-like codes. This paper also presents a technique which performs the entire calculation of the SP59 bound in the logarithmic domain, thus facilitating the exact calculation of this bound for moderate to large block lengths without the need for the asymptotic approximations provided by Shannon.     

On Achievable Rates and Complexity of LDPC Codes Over Parallel Channels: Bounds and Applications

A variety of communication scenarios can be modeled by a set of parallel channels. Upper bounds on the achievable rates under maximum-likelihood (ML) decoding, and lower bounds on the decoding complexity per iteration of ensembles of low-density parity-check (LDPC) codes are presented. The communication of these codes is assumed to take place over statistically independent parallel channels where the component channels are memoryless, binary-input, and output-symmetric. The bounds are applied to ensembles of punctured LDPC codes where the puncturing patterns are either random or possess some structure. Our discussion is concluded by a diagram showing interconnections between the new theorems and some previously reported results     

多径衰落信道下LDPC码初始译码消息研究

LDPC码初始译码消息是LDPC码密度演进研究的必要条件。本文简述了LDPC码的相关基础知识．重点研究了Rician衰落信道及Rayleigh信道下LDPC码的初始译码消息的概率密度．给出了译码消息的对称性和稳定性的表达，探讨了BP和BP_based两种译码方法的初始消息的概率密度形式，对于不同信道参数和译码算法下的初始消息的概率聚集函数（PMF：Probability Mass Function）进行了比较。     

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.     

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.     

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.     

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.     

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。     

Combine LDPC Codes Over GF(q) With q-ary Modulations for Bandwidth Efficient Transmission

Low-density parity-check (LDPC) codes are playing more and more important role in digital broadcasting standards due to their excellent error correction performance. In this paper, we study the combination of LDPC codes over GF(q) with q-ary modulations for bandwidth efficient transmission over AWGN channel and consider the design of the codes. Specifically, we develop the concept of quasi-regular codes, and propose an improved Monte Carlo method to optimize the quasi-regular codes. To justify the performance of our proposed scheme, simulation results are presented and analysed.     

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.