LDPC码和-积解码算法研究

首先介绍了LDPC 码的校验矩阵和其因子表示方法,然后利用二分图对和积解码算法进行了详细的描述,最后给出了信度传播概率译码算法详细步骤,并对关键公式作了证明。     

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。     

基于稀疏二进制序列的低密度奇偶校验码

通过对低密度奇偶校验(LDPC)码构造的研究,提出了一种利用稀疏二进制序列构造规则LDPC码的新颖而简单的方法。在构造中,还提出了奇偶校验矩阵里元素‘1’的分布矩阵的概念。为了确保码Tanner图的最小圈长为8,利用了序列的周期自相关函数和周期互相关函数。通过仿真表明构造的新码在和积算法下进行迭代解码性能优异。由于产生的LDPC码本身固有的准循环结构,还能得到较低的编码复杂度。     

异步编码CDMA系统中基于因子图的迭代多用户接收器

针对异步编码CDMA系统，本文提出了一种基于因子图的迭代多用户接收器，它是将用户信息比特对接收端噪声白化滤波器输出的条件后验概率分布用因子图表示，并采用和-积算法，经过有限次迭代获得用户信息比特的估计值．为降低计算复杂度，本文还提出一种简化算法．仿真结果表明，本文提出的迭代多用户接收器在经过几次迭代后的比特误码性能接近单用户系统；同时，简化算法的性能接近完全算法，但算法复杂度有明显改善．     

LDPC码在因子图上的构造及其译码

LDPC码是一种可以接近香农限的线性分组码,可通过稀疏奇偶校验矩阵来构造。也可以用因子图来构成。根据LDPC码的不同构成方法至今已提出了数种不同的译码方法。本文介绍了基于因子图的LDPC码的构造方法,分析了和一积(SPA)译码算法的基本原理,最后详细讨论了用SPA算法对LDPC码进行译码的过程。     

基于因子图的分布式变分稀疏贝叶斯压缩感知简

提出了一种基于因子图的分布式变分稀疏贝叶斯压缩感知算法。该算法利用因子图和变分方法将全局感知问题分解为简单的局部问题,通过认知用户邻居间的置信传播实现“软融合”,使每个认知用户能够获得全局最优估计。且充分利用邻居间传递的信息所具有的时间和空间二维相关性,提高认知用户在低信噪比下的感知性能。同时,算法在迭代过程中自适应地删除不收敛的超参数及对应的基函数,降低通信负载。实验结果表明：该方法在低采样率和低信噪比下有较好的感知性能。     

AWGN信道下Turbo码解码算法的选择

在加性高斯白噪声（AWGN）信道下,采用最大后验概率(MAP)算法的Turbo码解码是误比特率最低的算法。为了降低运算量实现快速解码,Log-MAP算法、Max-Log-Map算法和线性Max-Log-Map算法分别对MAP算法进行了不同程度的简化。本文简单介绍了基于MAP算法的Turbo码解码原理,从纠正函数的角度出发归纳和比较了三种MAP类简化算法,通过纠正函数从理论上对算法性能以及对信噪比估计误差的敏感度进行了分析,对分析结果进行了仿真验证。综合解码性能和运算量,提出了Turbo码解码的算法选择方案,以及实用,简易的Turbo码解码参数设置建议。      

DME中的莫尔斯码软件解码的探讨

在 DME 系统中，地面台的识别码是一种莫尔斯码编码。本文在分析该莫尔斯码的解码原理和比较两种解码方案的基础上，给出软件解码的算法和可行性方案，实现了莫尔斯码的准确解码。     

基于ZEVIO 1030的JPEG解码算法实现

概述了JPEG图像解码算法的基本原理,论述了JPEG图像解码算法基于双核处理器ZEVIO 1030的实现过程,并跟据ZEVIO 1030处理器中ARM9和ZSP400的通信机制,对JPEG解码算法进行优化,实现高效解码.     

基于自身可信度的低复杂度LDPC码位翻转解码算法

提出一种基于位翻转的低复杂度、便于硬件实现的LDPC码解码算法.该算法充分利用变量节点的本征信息来计算翻转判决函数,减少了对其它变量节点软信息的需求,因此大大降低了解码硬件实现的复杂度,同时保证翻转判决函数具有较高的可靠性.利用该算法,对RS-based LDPC码进行的仿真结果表明,改进算法的解码性能接近甚至略优于IMWBF算法.     

Codes defined on graphs

Low-density parity-check codes, turbo codes, and indeed most practically decodable capacity-approaching error correcting codes can all be understood as codes defined on graphs. Graphs not only describe the codes, but, more important, they structure the operation of the sum-product decoding algorithm (or one of many possible variations), which can be used for iterative decoding. Such coding schemes have the potential to approach channel capacity, while maintaining reasonable decoding complexity. In this tutorial article we review factor graphs, which can be used to describe codes and the joint probability distributions that must be dealt with in decoding. We also review the sum-product algorithm, and show how this algorithm leads to iterative decoding algorithms for codes defined on graphs.     

Factor graphs and the sum-product algorithm

Algorithms that must deal with complicated global functions of many variables often exploit the manner in which the given functions factor as a product of “local” functions, each of which depends on a subset of the variables. Such a factorization can be visualized with a bipartite graph that we call a factor graph, In this tutorial paper, we present a generic message-passing algorithm, the sum-product algorithm, that operates in a factor graph. Following a single, simple computational rule, the sum-product algorithm computes-either exactly or approximately-various marginal functions derived from the global function. A wide variety of algorithms developed in artificial intelligence, signal processing, and digital communications can be derived as specific instances of the sum-product algorithm, including the forward/backward algorithm, the Viterbi algorithm, the iterative “turbo” decoding algorithm, Pearl's (1988) belief propagation algorithm for Bayesian networks, the Kalman filter, and certain fast Fourier transform (FFT) algorithms     

Codes on graphs: normal realizations

A generalized state realization of the Wiberg (1996) type is called normal if symbol variables have degree 1 and state variables have degree 2. A natural graphical model of such a realization has leaf edges representing symbols, ordinary edges representing states, and vertices representing local constraints. Such a graph can be decoded by any version of the sum-product algorithm. Any state realization of a code can be put into normal form without essential change in the corresponding graph or in its decoding complexity. Group or linear codes are generated by group or linear state realizations. On a cycle-free graph, there exists a well-defined minimal canonical realization, and the sum-product algorithm is exact. However, the cut-set bound shows that graphs with cycles may have a superior performance-complexity tradeoff, although the sum-product algorithm is then inexact and iterative, and minimal realizations are not well-defined. Efficient cyclic and cycle-free realizations of Reed-Muller (RM) codes are given as examples. The dual of a normal group realization, appropriately defined, generates the dual group code. The dual realization has the same graph topology as the primal realization, replaces symbol and state variables by their character groups, and replaces primal local constraints by their duals. This fundamental result has many applications, including to dual state spaces, dual minimal trellises, duals to Tanner (1981) graphs, dual input/output (I/O) systems, and dual kernel and image representations. Finally a group code may be decoded using the dual graph, with appropriate Fourier transforms of the inputs and outputs; this can simplify decoding of high-rate codes     

Analogue decoding of tail-biting convolutional codes based on tanner graph

A scheme is proposed to decode a tail-biting convolutional code based on its Tanner graph, which is traditionally done using a forward-backward MAP algorithm. Therefore, decoding may be performed using a standard sum-product algorithm. With respect to decoding based on trellis, all variables in a Tanner graph are binary, which may lead to complexity reduction. A min-sum algorithm is used to decrease the analogue circuit complexity. Simulation shows there is no significant degradation compared with more complex traditional methods     

无线光通信下极化码DNN-NOMS译码方法研究

针对无线光通信中大气湍流引起极化码置信度传播译码性能不佳的问题,提出了一种无线光通信下极化码DNN-NOMS （Deep Neural Networks-Normalized and Offset Min-Sum）译码方法。首先,把传统的极化码置信传播译码算法因子图转化为类似于低密度奇偶校验（Low-density Parity Check, LDPC）码的Tanner图,在Tanner图展开并转化为深度神经网络（DNN）图形表示的基础上,将MS（Min-Sum）译码方法同时添加归一化因子和偏移因子来给Tanner图的边赋予权重,简化极化码对数似然比的计算方法,通过限制训练参数的数量,选取在损失函数最小的条件下的因子参数,训练得到最优归一化因子和偏移因子的译码模型。仿真结果表明,在不同的大气湍流强度下,该译码方法以牺牲较小的存储空间为前提的情况下能选取更优的归一化因子和偏移因子参数,从而获得更好的误码率性能,且大幅度降低译码复杂度;在误码率为10?4时,DNN-NOMS译码方法能产生0.21~3.56 dB的性能增益,且将迭代次数的运算次数降低87.5%。     

Using linear programming to Decode Binary linear codes

A new method is given for performing approximate maximum-likelihood (ML) decoding of an arbitrary binary linear code based on observations received from any discrete memoryless symmetric channel. The decoding algorithm is based on a linear programming (LP) relaxation that is defined by a factor graph or parity-check representation of the code. The resulting "LP decoder" generalizes our previous work on turbo-like codes. A precise combinatorial characterization of when the LP decoder succeeds is provided, based on pseudocodewords associated with the factor graph. Our definition of a pseudocodeword unifies other such notions known for iterative algorithms, including "stopping sets," "irreducible closed walks," "trellis cycles," "deviation sets," and "graph covers." The fractional distance d/sub frac/ of a code is introduced, which is a lower bound on the classical distance. It is shown that the efficient LP decoder will correct up to /spl lceil/d/sub frac//2/spl rceil/-1 errors and that there are codes with d/sub frac/=/spl Omega/(n/sup 1-/spl epsi//). An efficient algorithm to compute the fractional distance is presented. Experimental evidence shows a similar performance on low-density parity-check (LDPC) codes between LP decoding and the min-sum and sum-product algorithms. Methods for tightening the LP relaxation to improve performance are also provided.     

On concatenated zigzag codes and their decoding schemes

In this letter, we show that a concatenated zigzag code can be viewed as a low-density parity-check (LDPC) code. Based on the bipartite graph representation for such a parallel-concatenated code, various sum-product based decoding algorithms are introduced and compared. The results show that the improved versions of sum-product algorithm exhibit better convergence rate while maintaining the essential parallel form.