基于LDPC码的BICM系统性能分析

低密度校验码(LDPC)由于其编码增益高、译码速度快、性能接近香农限的优点,目前得到学术界的广泛关注.文中简单介绍了LDPC码及其译码算法,在此基础上结合比特交织编码调制(BICM)系统,并在算法上作出了相应改进.仿真结果表明,在高斯信道、充分交织瑞利信道、相关瑞利衰落信道下,此算法正确有效.     

基于非规则LDPC码的图像传输性能

LDPC码性能非常逼近香农极限且实现复杂度低,具有很强的纠错抗干扰能力,几乎适用于所有信道。在此采用DVB-S2标准中LDPC码的构造和编码方案,重点研究了LDPC码的译码原理,并将其用于加性高斯白噪声信道（AWGN Channel）图像的传输中。仿真结果表明在非规则LDPC码在低信噪比情况下,能为图像传输带来显著性能提高,且系统复杂度低,译码时延短。     

低密度校验码及其在图像传输中的应用

低密度校验(Low-Density Parity-Check,LDPC)码是一种基于图和迭代译码的信道编码方案,性能非常接近Shannon极限且实现复杂度低,具有很强的纠错抗干扰能力。该文深入研究了LDPC码的编码和译码基本原理,并将其应用于移动衰落信道图像的传输中,仿真结果表明LDPC码能为图像传输带来显著的性能提高,且系统复杂度低,译码时延短。     

Optimized low density parity check codes designs for half duplex relay channels

We propose in this paper optimized designs for LDPC codes which are able to work close to the theoretical bounds for the half duplex relay channel using the decode and forward strategy originally proposed by Cover and El Gamal. The challenge is that we have to find two codes operating at different rates and at different SNR?s: one for source-destination and the other for relay-destination transmission. We use density evolution together with Gaussian approximation for the design of the proposed irregular LDPC codes. Simulation results show that our proposed LDPC enable to work within less than 1.0 dB from the theoretical limit capacities under different channel conditions.     

Unequal Error Protection Using Partially Regular LDPC Codes

In this paper, we propose a scheme to construct low-density parity-check (LDPC) codes that are suitable for unequal error protection (UEP). We derive density evolution (DE) formulas for the proposed unequal error protecting LDPC ensembles over the binary erasure channel (BEC). Using the DE formulas, we optimize the codes. For the finite-length cases, we compare our codes with some other LDPC codes, the time-sharing method, and a previous work on UEP using LDPC codes. Simulation results indicate the superiority of the proposed design methodology for UEP     

Performance analysis and code optimization of low densityparity-check codes on Rayleigh fading channels

A numerical method has been presented to determine the noise thresholds of low density parity-check (LDPC) codes that employ the message passing decoding algorithm on the additive white Gaussian noise (AWGN) channel. In this paper, we apply the technique to the uncorrelated flat Rayleigh fading channel. Using a nonlinear code optimization technique, we optimize irregular LDPC codes for such a channel. The thresholds of the optimized irregular LDPC codes are very close to the Shannon limit for this channel. For example, at rate one-half, the optimized irregular LDPC code has a threshold only 0.07 dB away from the capacity of the channel. Furthermore, we compare simulated performance of the optimized irregular LDPC codes and turbo codes on a land mobile channel, and the results indicate that at a block size of 3072, irregular LDPC codes can outperform turbo codes over a wide range of mobile speeds     

On construction of rate-compatible low-density Parity-check codes

In this letter, we present a framework for constructing rate-compatible low-density parity-check (LDPC) codes. The codes are linear-time encodable and are constructed from a mother code using puncturing and extending. Application of the proposed construction to a type-II hybrid automatic repeat request (ARQ) scheme with information block length k=1024 and code rates 8/19 to 8/10, using an optimized irregular mother code of rate 8/13, results in a throughput which is only about 0.7 dB away from Shannon limit. This outperforms existing similar schemes based on turbo codes and LDPC codes by up to 0.5 dB.     

Performance of low density parity check coded continuous phase frequency shift keying (LDPCC‐CPFSK) over fading channels

In this paper, in order to improve bit error performance, bandwidth efficiency and reduction of complexity compared to related schemes such as turbo codes, we combine low density parity check (LDPC) codes and continuous phase frequency shift keying (CPFSK) modulation and introduce a new scheme, called ‘low density parity check coded‐continuous phase frequency shift keying (LDPCC‐CPFSK)’. Since LDPC codes have very large Euclidean distance and use iterative decoding algorithms, they have high error correcting capacity and have very close performances to Shannon limit. In all communication systems, phase discontinuities of modulated signals result extra bandwidth requirements. Continuous phase modulation (CPM) is a powerful solution for this problem. Beside CPM provides good bandwidth efficiency; it also improves bit error performance with its memory unit. In our proposed scheme, LDPC and CPFSK, which is a special type of CPM, are considered together to improve both error performance and bandwidth efficiencies. We also obtain error performance curves of LDPCC‐CPFSK via computer simulations for both regular and irregular LDPC code. Simulation results are drawn for 4‐ary CPFSK, 8‐ary CPFSK and 16‐ary CPFSK over AWGN, Rician and Rayleigh fading channels for maximum 100 iterations, while the frame size is chosen as 504. Copyright © 2006 John Wiley & Sons, Ltd.     

Construction of quasi‐cyclic low‐density parity‐check codes with low encoding complexity

Low encoding complexity is very important for quasi‐cyclic low‐density parity‐check (QC‐LDPC) codes used in wireless communication systems. In this paper, a new scheme is presented to construct QC‐LDPC codes with low encoding complexity. This scheme is called two‐stage particle swarm optimization (TS‐PSO) algorithm, in which both the threshold and girth distribution of QC‐LDPC codes are considered. The proposed scheme is composed of two stages. In the first stage, we construct a binary base matrix of QC‐LDPC code with the best threshold. The matrix is constructed by combining a binary PSO algorithm and the protograph extrinsic information transfer (PEXIT) method. In the second stage, we search an exponent matrix of the QC‐LDPC code with the best girth distribution. This exponent matrix is based on the base matrix obtained in the first stage. Consequently, the parity‐check matrix of the QC‐LDPC code with the best threshold and best girth distribution are constructed. Furthermore, bit error rate performances are compared for the QC‐LDPC codes constructed by proposed scheme, the QC‐LDPC code in 802.16e standard, and the QC‐LDPC code in Tam's study. Simulation results show that the QC‐LDPC codes proposed in this study are superior to both the 802.16e code and the Tam code on the additive white Gaussian noise (AWGN) and Rayleigh channels. Moreover, proposed scheme is easily implemented, and is flexible and effective for constructing QC‐LDPC codes with low encoding complexity. Copyright © 2012 John Wiley & Sons, Ltd.     

低复杂度的LDPC码联合编译码构造方法研究

LDPC码因为其具有接近香农限的译码性能和适合高速译码的并行结构,已经成为纠错编码领域的研究热点。LDPC码校验矩阵的构造是基于稀疏的随机图,所以该类码字编码和译码的硬件实现比较复杂。以单位阵的循环移位阵为基本单元,构造LDPC码的校验矩阵,降低了LDPC码在和积算法下的译码复杂度。同时考虑到LDPC码的编码复杂度,给出了一种可以简化编码的结构。针对该方案构造的LDPC码,提出了消除其二分图上的短圈的方法。通过大量的仿真和计算分析,本文比较了这种LDPC码和随机构造的LDPC码在误码率性能,圈长分布以及最小码间距估计上的差异。     

Memory-efficient sum-product decoding of LDPC codes

Low-density parity-check (LDPC) codes perform very close to capacity for long lengths on several channels. However, the amount of memory (fixed-point numbers that need to be stored) required for implementing the message-passing algorithm increases linearly as the number of edges in the graph increases. In this letter, we propose a decoding algorithm for decoding LDPC codes that reduces the memory requirement at the decoder. The proposed decoding algorithm can be analyzed using density evolution; further, we show how to design good LDPC codes using this. Results show that this algorithm provides almost the same performance as the conventional sum-product decoding of LDPC codes.     

Design of Quasi-Cyclic LDPC codes based on Euclidean Geometries

A new method for constructing Quasi-Cyclic (QC) Low-Density Parity-Check (LDPC) codes based on Euclidean Geometry (EG) is presented. The proposed method results in a class of QC-LDPC codes with girth of at least 6 and the designed codes perform very close to the Shannon limit with iterative decoding. Simulations show that the designed QC-LDPC codes have almost the same performance with the existing EG-LDPC codes.     

Construction of Irregular LDPC Codes by Quasi-Cyclic Extension

In this correspondence, we propose an approach to construct irregular low-density parity-check (LDPC) codes based on quasi-cyclic extension. When decoded iteratively, the constructed irregular LDPC codes exhibit a relatively low error floor in the high signal-to-noise ratio (SNR) region and are subject to relatively few undetected errors. The LDPC codes constructed based on the proposed scheme remain efficiently encodable     

基于低密度校验码的OFDM编码调制译码算法

低密度校验码(LDPC)具有编码增益高、译码速度快、性能接近Shannon限的优点。LDPC码应用于OFDM，能有效地提高多径环境下OFDM的BER性能。本文首先简单介绍LDPC码及其概率域上的译码算法，在此基础上对译码算法作融合，阐述概率似然比的译码算法。为了把LDPC应用于OFDM系统上，提出了多电平调制下的LDPC译码的算法。仿真结果表明，在AWGN和Rayleigh信道下，此算法正确有效。     

Parallel Weighted Bit-Flipping Decoding

A parallel weighted bit-flipping (PWBF) decoding algorithm for low-density parity-check (LDPC) codes is proposed. Compared to the best known serial weighted bit-flipping decoding, the PWBF decoding converges significantly faster but with little performance penalty. For decoding of finite-geometry LDPC codes, we demonstrate through examples that the proposed PWBF decoding converges in about 5 iterations with performance very close to that of the standard belief-propagation decoding.     

LDPC码在802.16a OFDM系统 衰落信道中的性能分析

本文通过对802.16a OFDM系统信道的分析,权衡估计的性能和算法复杂度两个因素,针对不同的传输环境,提出了动态的OFDM信道估计方案.另外我们找到了一组优秀的非正则LDPC码,将其应用于IEEE 802.16a OFDM环境中,仿真验证了它们在SUI-3和SUI-5多径衰落信道环境下具有良好的性能,并和协议中提出的卷积Turbo码进行了比较,结果证明在相同条件下,本文的LDPC码可以取得比协议提出的卷积Turbo码更优越的性能,具有更好的抗多径衰落的能力.     

Design of multi-input multi-output systems based on low-density Parity-check codes

We design serial concatenated multi-input multi-output systems based on low-density parity-check (LDPC) codes. We employ a receiver structure combining the demapper/detector and the decoder in an iterative fashion. We consider the a posteriori probability (APP) demapper, as well as a suboptimal demapper incorporating interference cancellation with linear filtering. Extrinsic information transfer (EXIT) chart analysis is applied to study the convergence behavior of the proposed schemes. We show that EXIT charts match very well with the simulated decoding trajectories, and they help explain the impact of different mappings and different demappers. It is observed that if the APP demapper transfer characteristics are almost flat, the LDPC codes optimized for binary-input channels are good enough to achieve performance close to the channel capacity. We also present a simple code-optimization method based on EXIT chart analysis, and we design a rate-1/2 LDPC code that achieves very low bit-error rates within 0.15 dB of the capacity of a two-input two-output Rayleigh fading channel with 4-pulse amplitude modulation. We next propose to use a space-time block code as an inner code of our serial concatenated coding scheme. By means of a simple example scheme, using an Alamouti inner code, we demonstrate that the design/optimization of the outer code (e.g., LDPC code) is greatly simplified.     

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.     

GB20600标准的LDPC码的改进

尽管LDPC码已经被GB20600标准采纳作为信道编码,与其它LDPC码相比,在同样码长和码率的情况下,GB20600 LDPC码误码率性能并非最佳;GB20600标准的LDPC码的码长达7493,存在编码复杂性问题,但是GB20600 LDPC码未采用基于校验矩阵的快速算法,这给GB20600 LDPC编解码器的硬件实现带来较大的困难。本文在现有GB20600 LDPC码的设计框架下,对GB20600中LDPC码的校验矩阵进行了修改,在此基础上提出一种有效的LDPC码的快速迭代算法,使编解码器的硬件易于实现。改进后的LDPC码的编码算法具有较低的实现复杂度。仿真结果表明,改进后的LDPC码的误包率性能优于现GB20600中LDPC码的误包率性能。      

Construction of Regular and Irregular LDPC Codes: Geometry Decomposition and Masking

Two algebraic methods for systematic construction of structured regular and irregular low-density parity-check (LDPC) codes with girth of at least six and good minimum distances are presented. These two methods are based on geometry decomposition and a masking technique. Numerical results show that the codes constructed by these methods perform close to the Shannon limit and as well as random-like LDPC codes. Furthermore, they have low error floors and their iterative decoding converges very fast. The masking technique greatly simplifies the random-like construction of irregular LDPC codes designed on the basis of the degree distributions of their code graphs