H-ARQ信道上高性能全分集LDPC码的构造与性能分析

为了提高混合自动重传请求(H-ARQ)系统的通信性能,研究了H-ARQ块衰落信道上全分集低密度奇偶校验(LDPC)码的构造与性能.首先分析了H-ARQ块衰落信道的中断概率及其固有分集,然后构造了在H-ARQ块衰落信道上能取得全分集的LDPC码,新构造的码字采用根校验节点把每次传输联系起来,从而获得全分集.在此基础上,分析了全分集LDPC码的结构,提出了通过提高全分集校验比特的比例,改善全分集LDPC码在H-ARQ信道上编码增益的方法.仿真结果表明,所提算法在H-ARQ信道上不仅能取得全分集,而且具有较高的编码增益     

编码协作MARC上全分集LDPC码的实现与性能分析

本文研究了多接入中继信道(MARC)上全分集LDPC码的实现与性能。首先,分析了MARC模型及其固有分集,然后构造了在MARC上能取得全分集的LDPC码,新构造的码字采用根校验节点把源节点传输与中继节点传输联系起来,从而获得全分集。接着,研究了所构造码字的密度演化过程,在密度演化的基础上,进一步分析了全分集LDPC码校验矩阵的结构,给出了通过提高全分集校验比特的比例,改善全分集LDPC码在MARC上编码增益的方法。仿真结果表明,本文所提算法在MARC信道上不仅能实现全分集,而且能取得较高的编码增益。     

LDPC码译码算法及性能分析

为了进一步降低低密度奇偶校验(LDPC)码译码算法的复杂度,基于经典置信传播(BP)译码算法,给出了对数域迭代后验概率对数似然比(APP LLR)算法。通过概率域的和积算法(SPA)和对数域的迭代APP LLR算法的性能仿真及分析可见,迭代APP LLR算法能以较小的性能损失换取复杂度的大幅降低。进一步选用迭代APP LLR算法,结合不同地形条件下的VHF频段信道模型,仿真了LDPC码编译码系统的性能。理论分析及仿真结果均表明,基于迭代APP LLR算法的LDPC码,实现简单,性能优异,具有良好的工程应用前景。     

On the performance of high-rate TPC/SPC codes and LDPC codes overpartial response channels

This paper evaluates two-dimensional turbo product codes based on single-parity check codes (TPC/SPC) and low-density parity check (LDPC) codes for use in digital magnetic recording systems. It is first shown that the combination of a TPC/SPC code and a precoded partial response (PR) channel results in a good distance spectrum due to the interleaving gain. Then, density evolution is used to compute the thresholds for TPC/SPC codes and LDPC codes over PR channels. Analysis shows that TPC/SPC codes have a performance close to that of LDPC codes for large codeword lengths. Simulation results for practical block lengths show that TPC/SPC codes perform as well as LDPC codes in terms of bit error rate, but possess better burst error statistics which is important in the presence of an outer Reed-Solomon code. Further, the encoding complexity of TPC/SPC codes is only linear in the codeword length and the generator matrix does not have to be stored explicitly. Based on. the results in the paper and these advantages, TPC/SPC codes seem like a viable alternative to LDPC codes     

多元LDPC码与二元LDPC码的性能分析

为了比较多元LDPC码与二元LDPC码的性能,文章从校验矩阵、Tanner图、BP译码算法等方面将两者进行有效的分析,并结合具体的Monte Carlo仿真实验,得出多元LDPC码的性能确实优于等长度码长的二元LDPC码.     

Design and analysis of nonbinary LDPC codes for arbitrary discrete-memoryless channels

We present an analysis under the iterative decoding of coset low-density parity-check (LDPC) codes over GF(q), designed for use over arbitrary discrete-memoryless channels (particularly nonbinary and asymmetric channels). We use a random- coset analysis to produce an effect that is similar to output symmetry with binary channels. We show that the random selection of the nonzero elements of the GF(q) parity-check matrix induces a permutation-invariance property on the densities of the decoder messages, which simplifies their analysis and approximation. We generalize several properties, including symmetry and stability from the analysis of binary LDPC codes. We show that under a Gaussian approximation, the entire q-1-dimensional distribution of the vector messages is described by a single scalar parameter (like the distributions of binary LDPC messages). We apply this property to develop extrinsic information transfer (EXIT) charts for our codes. We use appropriately designed signal constellations to obtain substantial shaping gains. Simulation results indicate that our codes outperform multilevel codes at short block lengths. We also present simulation results for the additive white Gaussian noise (AWGN) channel, including results within 0.56 dB of the unrestricted Shannon limit (i.e., not restricted to any signal constellation) at a spectral efficiency of 6 bits/s/Hz.     

LDPC codes for fading Gaussian broadcast channels

In this work, we study coding over a class of two-user broadcast channels (BCs) with additive white Gaussian noise and multiplicative fading known at the receivers only. Joint decoding of low-density parity-check (LDPC) codes is analyzed. The message update rule at the mapping node linking the users' codes is derived and is found to exhibit an interesting soft interference cancellation property. High performance codes are found using the differential evolution optimization technique and extrinsic information transfer analysis adapted to our multiuser setting. The optimized codes have rates very close to the boundary of the achievable region for binary constrained input for both faded and unfaded channels. Simulation results for moderate block lengths show that our codes operate within less than 1 dB of their respective threshold.     

Raptor codes on binary memoryless symmetric channels

In this paper, we will investigate the performance of Raptor codes on arbitrary binary input memoryless symmetric channels (BIMSCs). In doing so, we generalize some of the results that were proved before for the erasure channel. We will generalize the stability condition to the class of Raptor codes. This generalization gives a lower bound on the fraction of output nodes of degree 2 of a Raptor code if the error probability of the belief-propagation decoder converges to zero. Using information-theoretic arguments, we will show that if a sequence of output degree distributions is to achieve the capacity of the underlying channel, then the fraction of nodes of degree 2 in these degree distributions has to converge to a certain quantity depending on the channel. For the class of erasure channels this quantity is independent of the erasure probability of the channel, but for many other classes of BIMSCs, this fraction depends on the particular channel chosen. This result has implications on the "universality" of Raptor codes for classes other than the class of erasure channels, in a sense that will be made more precise in the paper. We will also investigate the performance of specific Raptor codes which are optimized using a more exact version of the Gaussian approximation technique.     

半双工中继信道下联合LDPC码设计

为了提高解码前传半双工中继通信系统的编码增益,提出了一种联合LDPC码编码结构及其度分布优化方法。该结构视信源和中继子码为联合LDPC码的一部分,目的端根据从信源和中继接收的消息进行联合译码,同时获得信源和中继的信息。为了分析联合LDPC码的渐进性能,推导了AWGN信道下联合LDPC码的高斯近似密度进化算法。结合译码收敛条件和度分布约束关系,提出联合LDPC码的度分布优化问题。仿真结果表明：联合LDPC码的渐进性能及误码性能优于BE-LDPC码和独立处理（SP）码。     

Parity-check density versus performance of binary linear block codes over memoryless symmetric channels

We derive lower bounds on the density of parity-check matrices of binary linear codes which are used over memoryless binary-input output-symmetric (MBIOS) channels. The bounds are expressed in terms of the gap between the rate of these codes for which reliable communications is achievable and the channel capacity; they are valid for every sequence of binary linear block codes if there exists a decoding algorithm under which the average bit-error probability vanishes. For every MBIOS channel, we construct a sequence of ensembles of regular low-density parity-check (LDPC) codes, so that an upper bound on the asymptotic density of their parity-check matrices scales similarly to the lower bound. The tightness of the lower bound is demonstrated for the binary erasure channel by analyzing a sequence of ensembles of right-regular LDPC codes which was introduced by Shokrollahi, and which is known to achieve the capacity of this channel. Under iterative message-passing decoding, we show that this sequence of ensembles is asymptotically optimal (in a sense to be defined in this paper), strengthening a result of Shokrollahi. Finally, we derive lower bounds on the bit-error probability and on the gap to capacity for binary linear block codes which are represented by bipartite graphs, and study their performance limitations over MBIOS channels. The latter bounds provide a quantitative measure for the number of cycles of bipartite graphs which represent good error-correction codes.     

投影几何LDPC码的构造及其在MIMO-OFDM系统中的性能分析

简要介绍低密度奇偶校验码（LDPC码）的发展历史及其码结构，重点研究基于投影几何的LDPC码的系统化构造方法，并将其作为信道编码加入基于IEEE802．16d标准的MIMO-OFDM系统中进行仿真，与级联RS-CC码进行性能对比与分析。最后得出结论，投影几何LDPC码将有可能作为下一代无线通信系统的一项关键技术被广泛采用。     

On the application of LDPC codes to arbitrary discrete-memoryless channels

We discuss three structures of modified low-density parity-check (LDPC) code ensembles designed for transmission over arbitrary discrete memoryless channels. The first structure is based on the well-known binary LDPC codes following constructions proposed by Gallager and McEliece, the second is based on LDPC codes of arbitrary (q-ary) alphabets employing modulo-q addition, as presented by Gallager, and the third is based on LDPC codes defined over the field GF(q). All structures are obtained by applying a quantization mapping on a coset LDPC ensemble. We present tools for the analysis of nonbinary codes and show that all configurations, under maximum-likelihood (ML) decoding, are capable of reliable communication at rates arbitrarily close to the capacity of any discrete memoryless channel. We discuss practical iterative decoding of our structures and present simulation results for the additive white Gaussian noise (AWGN) channel confirming the effectiveness of the codes.     

LDPC码的稳定中断分析

对于一个给定的信道和一个特定的ldpc码族,针对由密度进化的不稳定性而造成的稳定中断事件,本文通过研究了BEC和AWGN信道中的稳定中断概率并确切表达了在块衰弱信道中的稳定中断概率,其仿真过程给出了在删除信道中容量逼近系统是怎样跳开了在块衰弱信道中的中断限制。     

LDPC码在相干光通信下的性能分析与研究

对于相干光通信系统,相位噪声成为影响系统性能的重要因素之一,并严重影响LDPC码(低密度奇偶校验码)软译码的性能。仿真结果表明,在16QAM调制方式下,500kHz线宽的激光器相位噪声将导致1.5dB的性能损失。为了降低相位噪声的影响,提出了一种基于相位噪声估计值修正LLR(对数似然比信息)的方法。经仿真验证,该LLR修正方法能够挽回0.5dB的译码性能损失。     

突发错误信道下的多元LDPC码设计与性能分析

分析比较了结构化非规则多元重复累计码、Turbo码和二元LDPC码在单突发删除信道和高斯突发深衰落信道上的纠错性能,同时提出了 QLDPC 在突发信道下的两条设计准则。针对突发信道设计了一类扩展型S-QIRA码—S-eQIRA,并在单突发删除信道和高斯突发深衰落信道上进行仿真,仿真结果表明该码字具有较强的纠突发错误能力。     

基于并行级联LDPC码的递增冗余HARQ方案及性能分析

并行级联LDPC码是由多个码率不同的子码,经并行级联后得到的码率可变的LDPC码.本文提出了基于并行级联:LDPC码的递增冗余HARQ方案,给出了这种方案的吞吐量性能封闭解.在AWGN信道和Rayleigh衰落信道下,通过仿真将新方案的性能和随机LDPC码的性能进行了比较.结果显示,并行级联LDPC码的递增冗余HARQ方案性能接近随机LDPC码,但编、译码更简单,参数选择范围更广.     

Progressive transmission of images over fading channels using rate-compatible LDPC codes.

In this paper, we propose a combined source/channel coding scheme for transmission of images over fading channels. The proposed scheme employs rate-compatible low-density parity-check codes along with embedded image coders such as JPEG2000 and set partitioning in hierarchical trees (SPIHT). The assignment of channel coding rates to source packets is performed by a fast trellis-based algorithm. We examine the performance of the proposed scheme over correlated and uncorrelated Rayleigh flat-fading channels with and without side information. Simulation results for the expected peak signal-to-noise ratio of reconstructed images, which are within 1 dB of the capacity upper bound over a wide range of channel signal-to-noise ratios, show considerable improvement compared to existing results under similar conditions. We also study the sensitivity of the proposed scheme in the presence of channel estimation error at the transmitter and demonstrate that under most conditions our scheme is more robust compared to existing schemes.     

Kikuchi approximation method for joint decoding of LDPC codes and partial-response channels

In this letter, we apply the Kikuchi approximation method to the problem of joint decoding of a low-density parity-check code and a partial-response channel. The Kikuchi method is, in general, more powerful than the conventional loopy belief propagation (BP) algorithm, and can produce better approximations to an underlying inference problem. We will first review the Kikuchi approximation method and the generalized BP algorithm, which is an iterative message-passing algorithm based on this method. We will then report simulation results which show that the Kikuchi method outperforms the best conventional iterative method.     

Dynamics and performance analysis of analog iterative decoding for low-density parity-check (LDPC) codes

Conventional iterative decoding with flooding or parallel schedule can be formulated as a fixed-point problem solved iteratively by a successive substitution (SS) method. In this paper, we investigate the dynamics of a continuous-time (asynchronous) analog implementation of iterative decoding, and show that it can be approximated as the application of the well-known successive relaxation (SR) method for solving the fixed-point problem. We observe that SR with the optimal relaxation factor can considerably improve the error-rate performance of iterative decoding for short low-density parity-check (LDPC) codes, compared with SS. Our simulation results for the application of SR to belief propagation (sum-product) and min-sum algorithms demonstrate improvements of up to about 0.7 dB over the standard SS for randomly constructed LDPC codes. The improvement in performance increases with the maximum number of iterations, and by accordingly reducing the relaxation factor. The asymptotic result, corresponding to an infinite maximum number of iterations and infinitesimal relaxation factor, represents the steady-state performance of analog iterative decoding. This means that under ideal circumstances, continuous-time (asynchronous) analog decoders can outperform their discrete-time (synchronous) digital counterparts by a large margin. Our results also indicate that with the assumption of a truncated Gaussian distribution for the random delays among computational modules, the error-rate performance of the analog decoder, particularly in steady state, is rather independent of the variance of the distribution. The proposed simple model for analog decoding, and the associated performance curves, can be used as an "ideal analog decoder" benchmark for performance evaluation of analog decoding circuits.     

Simplified sum-product algorithm for decoding LDPC codes with optimal performance

A simple, yet effective decoding algorithm is proposed for low-density parity-check (LDPC) codes, which significantly simplifies the check node update computation of the optimal sum-product algorithm. It achieves essentially optimal performance by applying scaling in the decoder?s extrinsic information. If no such scaling is applied, then the proposed algorithm has small performance degradation, e.g. in the order of 0.1 to 0.2 dB, depending on the coded block size.