对LDPC码的LLRBP算法研究

在LDPC译码时,使用IJLRBP算法其校验节点的计算复杂度十分高,而且当LDPC码中有许多的短环时,译码性能也会降低。基于以上的这些问题提出了一个新的混合校验变量过程,通过调整校验节点的处理振幅和变量节点的信息相关性来降低计算复杂度,其仿真过程表明在译码性能和运算复杂度上与LLRBP算法都有较大的提高。     

一种简化的LDPC码BP译码算法的研究

低密度奇偶校验码(LDPC码)是一种逼近香农限的线性分组码,译码的复杂度较低;在LDPC码译码算法中性能较好的是置信传播译码(BP)算法,他能够在迭代译码过程中确定码字是否已译出,但是复杂度高,运算量大。采用一种改进的BP译码算法,在迭代译码过程中对校验节点的更新信息进行曲线拟合,以减小译码运算量,有利于硬件的并行实现,减少译码延时。仿真结果表明,改进的BP算法译码性能和原来的BP算法接近,而且复杂度较低。     

A new high rate code scheme with highly parallel and low complexity decoding algorithm

A new high rate code scheme is proposed in this paper. It consists of serial concatenated recursive systematic ordinary (nonpunctured) convolutional codes with only 8 states in the trellis of the corresponding reciprocal dual codes. With a low complexity and highly parallel decoding algorithm, over additive white Gaussian noise channels, the proposed codes can achieve good bit error rate (BER) performance comparable to that of turbo codes and low density parity check (LDPC) codes. At code rate R=16/17, the overall decoding complexity of the proposed code scheme is almost half that of the LDPC codes.     

一种改进的无线光通信LDPC码译码算法

针对无线光通信中低密度奇偶校验码(LDPC)置信传播(BP)译码算法复杂度高及置信度振荡造成译码错误等缺点,基于对数BP算法提出了一种改进的译码算法。改进的译码算法在校验节点运算时,判断输入到校验节点消息的最小值与某个门限的大小,根据比较结果,分别用消息最小值或若干个最小值进行运算,在损失很少性能的情况下降低了运算复杂度;同时在比特节点采用振荡抵消处理运算,提高了算法的性能增益。最后在对数正态分布湍流信道模型下,分别对比特充分交织和交织深度为16的情况进行了仿真实验。仿真结果表明,改进的译码算法与BP算法相比,大幅度降低了计算复杂度,而且译码性能有一定的优势,收敛速度损失很少;而相对于最小和算法,改进的算法虽然译码复杂度有所增加,但误码率性能有明显的优势,并且收敛速度也优于最小和算法。因此,改进的译码算法是无线光通信中LDPC码译码算法复杂度和性能之间一个较好的折中处理方案。     

Iterative decoding of one-step majority logic deductible codesbased on belief propagation

Previously, the belief propagation (BP) algorithm has received a lot of attention in the coding community, mostly due to its near-optimum decoding for low-density parity check (LDPC) codes and its connection to turbo decoding. In this paper, we investigate the performance achieved by the BP algorithm for decoding one-step majority logic decodable (OSMLD) codes. The BP algorithm is expressed in terms of likelihood ratios rather than probabilities, as conventionally presented. The proposed algorithm fits better the decoding of OSMLD codes with respect to its numerical stability due to the fact that the weights of their check sums are often much higher than that of the corresponding LDPC codes. Although it has been believed that OSMLD codes are far inferior to LDPC codes, we show that for medium code lengths (say between 200-1000 bits), the BP decoding of OSMLD codes can significantly outperform BP decoding of their equivalent LDPC codes. The reasons for this behavior are elaborated     

FPGA implementation of low complexity LDPC iterative decoder

Low-density parity-check (LDPC) codes, proposed by Gallager, emerged as a class of codes which can yield very good performance on the additive white Gaussian noise channel as well as on the binary symmetric channel. LDPC codes have gained lots of importance due to their capacity achieving property and excellent performance in the noisy channel. Belief propagation (BP) algorithm and its approximations, most notably min-sum, are popular iterative decoding algorithms used for LDPC and turbo codes. The trade-off between the hardware complexity and the decoding throughput is a critical factor in the implementation of the practical decoder. This article presents introduction to LDPC codes and its various decoding algorithms followed by realisation of LDPC decoder by using simplified message passing algorithm and partially parallel decoder architecture. Simplified message passing algorithm has been proposed for trade-off between low decoding complexity and decoder performance. It greatly reduces the routing and check node complexity of the decoder. Partially parallel decoder architecture possesses high speed and reduced complexity. The improved design of the decoder possesses a maximum symbol throughput of 92.95 Mbps and a maximum of 18 decoding iterations. The article presents implementation of 9216 bits, rate-1/2, (3, 6) LDPC decoder on Xilinx XC3D3400A device from Spartan-3A DSP family.     

Iterative reliability-based decoding of low-density parity checkcodes

In this paper, reliability based decoding is combined with belief propagation (BP) decoding for low-density parity check (LDPC) codes. At each iteration, the soft output values delivered by the BP algorithm are used as reliability values to perform reduced complexity soft decision decoding of the code considered. This approach allows to bridge the error performance gap between belief propagation decoding which remains suboptimum, and maximum likelihood decoding which is too complex to be implemented for the codes considered. Trade-offs between decoding complexity and error performance are also investigated. In particular, a stopping criterion which reduces the average number of iterations at the expense of very little performance degradation is proposed for this combined decoding approach. Simulation results for several Gallager (1963, 1968) LDPC codes and different set cyclic codes of hundreds of information bits are given and elaborated     

A differential binary message-passing LDPC decoder

In this paper, we propose a binary message-passing algorithm for decoding low-density parity-check (LDPC) codes. The algorithm substantially improves the performance of purely hard-decision iterative algorithms with a small increase in the memory requirements and the computational complexity. We associate a reliability value to each nonzero element of the code's parity-check matrix, and differentially modify this value in each iteration based on the sum of the extrinsic binary messages from the check nodes. For the tested random and finite-geometry LDPC codes, the proposed algorithm can perform as close as about 1 dB and 0.5 dB to belief propagation (BP) at the error rates of interest, respectively. This is while, unlike BP, the algorithm does not require the estimation of channel signal to noise ratio. Low memory and computational requirements and binary message-passing make the proposed algorithm attractive for high-speed low-power applications.     

低密度校验码BP译码算法中量化问题的研究

本文对低密度校验(LDPC)码BP译码算法的量化问题(主要是接收比特信号和中间变量)进行了研究.着重讨论了量化范围、量化级数、均匀和非均匀量化等因素对译码性能的影响,给出了LDPC码BP译码算法的一些实用性的结论.并进一步发现在对BP译码算法的中间变量进行高阶量化处理时,在高信噪比的情况下,能明显地减小译码的误码率,降低译码算法的错误平层,提高译码性能.     

A high‐performance belief propagation decoding algorithm for codes with short cycles

The simplicity of decoding is one of the most important characteristics of the low density parity check (LDPC) codes. Belief propagation (BP) decoding algorithm is a well‐known decoding algorithm for LDPC codes. Most LDPC codes with long lengths have short cycles in their Tanner graphs, which reduce the performance of the BP algorithm. In this paper, we present 2 methods to improve the BP decoding algorithm for LDPC codes. In these methods, the calculation of the variable nodes is controlled by using “multiplicative correction factor” and “additive correction factor.” These factors are obtained for 2 separate channels, namely additive white Gaussian noise (AWGN) and binary symmetric channel (BSC), as 2 functions of code and channel parameters. Moreover, we use the BP‐based method in the calculation of the check nodes, which reduces the required resources. Simulation results show the proposed algorithm has better performance and lower decoding error as compared to BP and similar methods like normalized‐BP and offset‐BP algorithms.     

On decoding of low-density parity-check codes over the binary erasure channel

This paper investigates decoding of low-density parity-check (LDPC) codes over the binary erasure channel (BEC). We study the iterative and maximum-likelihood (ML) decoding of LDPC codes on this channel. We derive bounds on the ML decoding of LDPC codes on the BEC. We then present an improved decoding algorithm. The proposed algorithm has almost the same complexity as the standard iterative decoding. However, it has better performance. Simulations show that we can decrease the error rate by several orders of magnitude using the proposed algorithm. We also provide some graph-theoretic properties of different decoding algorithms of LDPC codes over the BEC which we think are useful to better understand the LDPC decoding methods, in particular, for finite-length codes.     

改进的离散字母表迭代译码算法研究

为了优化LDPC迭代译码性能和降低算法复杂度,提出了一种改进的基于Gallager A算法的2b离散字母表迭代译码算法。在每一轮迭代中,Tanner图上的校验节点与变量节点之间所传递的消息有1b表示符号值,另1b反映码字结构特性,其中变量节点更新规则是通过查表法来实现的。在二元对称信道下针对列重为3的规则LDPC码做了仿真实验,仿真结果表明该算法性能明显优于原算法,并且具有较低的复杂度。     

Efficient LDPC‐Based,Threaded Layered Space‐Time‐Frequency System with Iterative Receiver

We present a low‐density parity‐check (LDPC)‐based, threaded layered space‐time‐frequency system with emphasis on the iterative receiver design. First, the unbiased minimum mean‐squared‐error iterative‐tree‐search (U‐MMSE‐ITS) detector, which is known to be one of the most efficient multi‐input multi‐output (MIMO) detectors available, is improved by augmentation of the partial‐length paths and by the addition of one‐bit complement sequences. Compared with the U‐MMSE‐ITS detector, the improved detector provides better detection performance with lower complexity. Furthermore, the improved detector is robust to arbitrary MIMO channels and to any antenna configurations. Second, based on the structure of the iterative receiver, we present a low‐complexity belief‐propagation (BP) decoding algorithm for LDPC‐codes. This BP decoder not only has low computing complexity but also converges very fast (5 iterations is sufficient). With the efficient receiver employing the improved detector and the low‐complexity BP decoder, the proposed system is a promising solution to high‐data‐rate transmission over selective‐fading channels.     

Design of serial concatenated MSK schemes based on density evolution

We consider the design of convolutional codes and low density parity check (LDPC) codes with minimum-shift keying (MSK) when the receiver employs iterative decoding and demodulation. The main idea proposed is the design of coded schemes that are well matched to the iterative decoding algorithm being used rather than to hypothetical maximum-likelihood decoding. We first show that the design is crucially dependent on whether the continuous phase encoder (CPE) is realized in recursive form or in nonrecursive form. We then consider the design of convolutionally coded systems and low density parity check codes with MSK to obtain near-capacity performance. With convolutional codes, we show that it is possible to improve the performance significantly by using a mixture of recursive and nonrecursive realizations for the CPE. For low density parity check codes, we show that codes designed for binary phase shift keying are optimal for MSK only if the nonrecursive realization is used; for the recursive realization, we design new LDPC codes based on the concept of density evolution. We show that these codes outperform the best known codes for MSK and have lower decoding complexity.     

GF(2p)LDPC编码的相位调制OFDM系统在瑞利衰落信道的性能

OFDM是一项能有效对抗高速无线通信中多径衰落的关键技术，为了进一步提高OFDM系统的误码性能，许多信道编码技术已被应用于OFDM系统中，二元域LDPC码以其近香农限的误码性能和较低的译码复杂度成为研究的热点。在AWGN信道下，多元域LDPC码比等效码长的二元域LDPC码有更好的纠错性能。本文提出了一种将多元域LDPC码经过MPSK调制后用于OFDM系统的新方法。仿真结果表明，在多径衰落信道下，通过合理选择多元LDPC码域的阶数和调制的方法，多元域LDPC编码的高阶调制OFDM系统比等效码长的二元域LDPC编码OFDM系统具有更好的性能，并且由于采用了多元域LDPC的快速BP译码，译码复杂度只是稍有增加。     

置信传播译码算法的性能测度

本文基于树和有限状态机系统地推导了低密度校验码(LDPC)置信传播译码算法中的消息修正公式,引入了连续消息空间的概率测度,推导了常见二元对称信道输出分布和迭代过程中消息密度进化的计算公式,讨论了算法性能的参数化估计.这种计算分析工具可以用于独立于信道的算法收敛性分析,有助于设计LDPC码,有助于分析LDPC码译码器的量化效应并实现快速译码方案,使其获得在实时通信系统中的应用.     

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。     

基于原型图的低码率LDPC码最小和译码算法改进方案

低密度奇偶校验(LDPC)码的译码硬件实现方案大多采用计算复杂度较低的修正最小和(NMS)算法,然而对于低码率LDPC码,由于校验节点度数低,NMS算法的修正误差较大,导致其译码性能和标准的置信传播(BP)算法相比有较大差异。该文针对基于原图构造的一类低码率LDPC码,提出了在NMS迭代译码中结合震荡抵消(OSC)处理和多系数(MF)修正技术的方案。结合低码率原型图LDPC码行重分布差异较大的特点,MF修正算法可以有效地减少计算误差,从而改善译码性能。另外低码率原型图LDPC码的收敛较慢,而OSC处理则可以较好地抑制正反馈信息,进一步提高NMS算法的性能增益。仿真结果表明,对于此类低码率LDPC码, MF-OSC-NMS算法可以达到接近BP算法的性能。OSC处理和MF修正技术硬件实现简单,与NMS算法相比几乎没有增加计算复杂度,因此MF-OSC-NMS算法是译码算法复杂度和性能之间一个较好的折中处理方案。     

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。      

Hybrid Iterative Decoding for Low-Density Parity-Check Codes Based on Finite Geometries

In this letter, a two-stage hybrid iterative decoding algorithm which combines two iterative decoding algorithms is proposed to reduce the computational complexity of finite geometry low-density parity-check (FG-LDPC) codes. We introduce a fast weighted bit-flipping (WBF) decoding algorithm for the first stage decoding. If the first stage decoding fails, the decoding is continued by the powerful belief propagation (BP) algorithm. The proposed hybrid decoding algorithm greatly reduces the computational complexity while maintains the same performance compared to that of using the BP algorithm only.