两类新的线性分组码的译码

本文推广了Ｐｌｅｓｓ由四元线性分组码构造Ｇｏｌａｙ码和由三元（４，２，３）线性分组码构造三元（１２，６，６）Ｇｏｌａｙ码的投影方法，给出了由四元（ｎ，ｋ，ｄ）线性分组码构造的二元（４ｎ，ｎ＋２ｋ，≥ｍｉｎ（８，ｎ，２ｄ）线性分组码和由三元（ｎ，ｋ，ｄ）线性分组码构造的三元（３ｎ，ｎ＋ｋ，≥ｍｉｎ（ｎ，２ｄ，６）线性分组码，并根据所得码的结构给出了有效的最大似然译码算法。     

线性分组码的神经网络译码

介绍了神经网络与线性分组码之间的关系，并在文献[1]的基础上证明了软判决译码与求解能量函数最大值之间的等价性，然后以(7，4，3)汉明码为例介绍了神经网络在循环码硬判决、软判决译码中的应用。     

线性分组码与时空分组码级联的迭代译码

提出了线性分组码与时空分组码的级联编码方案,推导了时空分组码在比特级上的软输入软输出译码算法,进而给出了在线性分组码和时空分组码之间进行迭代译码的算法。仿真结果表明这种方案与现有方案相比在能够获得最大分集增益的同时还能获得更大的编码增益。     

一种线性分组码的查表译码法及其应用

针对纠正两个随机错误的线性分组码,采用重复查表译码法,通过多次查询含一个错误的伴随式与错误图样的译码表,实现了一种占有很少存储空间的查表译码算法。该算法在码长较短时译码的计算量较少,可适用于利用单片机等低运算能力情况下的通信应用中。文中对纠正2个错误的（26,16）缩短循环码的译码进行了实现,验证了算法的可行性。     

q元线性分组码的快速软判决译码

本文构造了一个三元有向树，由此导出了三元线性分组码的快速软判决译码算法。该算法充分利用分支限界技术，考查了包括全部错误图样在内的所有列图样，从而得到一个与接收序列欧氏距离最近的码字。模拟结果表明该算法具有较低的时间复杂度     

一类三元线性分组码的译码

Ｐｌｅｓｓ［１］证明了三元（１２，６，６）Ｇｏｌａｙ码具有一种双层结构，并据此给出了该码的快速硬判决译码算法。本文推广了Ｇｏｌａｙ码的Ｐｌｅｓｓ结构，给出了由三元（ｎ，ｋ，ｄ）线性分组码构造的三元（３，ｎ＋ｋ，≥ｍｉｎ（ｎ，２ｄ，６））线性分组码，其中包括（１２，６，６）Ｇｏｌａｙ码和（１８，９，６）码，并以三元（１８，９，６）码为例给出了这类码的最大似然软判决译码算法。     

软判决译码研究进展

本文综述了软判决译码研究的发展概况，全文分四部分。第一部分简单地回顾了构造Ｓｈａｎｎｏｎ码的发展概况；第二部分在前一部分基础上叙述了线性分组码软判决译码的一般研究的状况；第三部分讨论了基于网络图上的线性分组码软判决译码的发展概况；最后描述了Ｔｒｕｂｏ码与迭代反馈软判决译码的研究状况与今后的发展方向     

Iterative Approximate Linear Programming Decoding of LDPC Codes With Linear Complexity

The problem of low complexity linear programming (LP) decoding of low-density parity-check (LDPC) codes is considered. An iterative algorithm, similar to min-sum and belief propagation, for efficient approximate solution of this problem was proposed by Vontobel and Koetter. In this paper, the convergence rate and computational complexity of this algorithm are studied using a scheduling scheme that we propose. In particular, we are interested in obtaining a feasible vector in the LP decoding problem that is close to optimal in the following sense. The distance, normalized by the block length, between the minimum and the objective function value of this approximate solution can be made arbitrarily small. It is shown that such a feasible vector can be obtained with a computational complexity which scales linearly with the block length. Combined with previous results that have shown that the LP decoder can correct some fixed fraction of errors we conclude that this error correction can be achieved with linear computational complexity. This is achieved by first applying the iterative LP decoder that decodes the correct transmitted codeword up to an arbitrarily small fraction of erroneous bits, and then correcting the remaining errors using some standard method. These conclusions are also extended to generalized LDPC codes.      

线性分组码译码算法的快速性能分析

为了分析高斯白噪信道中线性分组码的译码性能,提出了采用低信噪比时数值仿真和高信噪比时理论估算相结合的方法来计算误码率,从而快速准确地获取整个信噪比范围内的译码性能曲线.试验结果表明,该方法得到的误码率与实际误码率一致.     

Nonlinear Programming Approaches to Decoding Low-Density Parity-Check Codes

We consider the decoding problem for low-density parity-check codes, and apply nonlinear programming methods. This extends previous work using linear programming (LP) to decode linear block codes. First, a multistage LP decoder based on the branch-and-bound method is proposed. This decoder makes use of the maximum-likelihood-certificate property of the LP decoder to refine the results when an error is reported. Second, we transform the original LP decoding formulation into a box-constrained quadratic programming form. Efficient linear-time parallel and serial decoding algorithms are proposed and their convergence properties are investigated. Extensive simulation studies are performed to assess the performance of the proposed decoders. It is seen that the proposed multistage LP decoder outperforms the conventional sum-product (SP) decoder considerably for low-density parity-check (LDPC) codes with short to medium block length. The proposed box-constrained quadratic programming decoder has less complexity than the SP decoder and yields much better performance for LDPC codes with regular structure.     

Sliding Block Decoding of Convolutional Codes

It is shown that a convolutional code can be decoded with a sliding-block decoder, a time-invariant nonlinear digital filter with finite memory and delay. If the memory and delay are small, then the sliding-block decoder can be implemented as a table lookup procedure in ROM, resulting in a low cost, high speed, and high reliability decoder.     

分组码的软判决伪序列译码

本文提出一种在形式上类似于卷积码的序列译码的一般线性分组码的软判决伪序列译码算法，利用广义限译码原理及二元有向树的性质与分枝限搜索技术，降低了译码复杂性，其设备复杂度小于Ｃｈａｓｅ译码器，模拟结果表明，该算法的误码输出性能接近维持比较最大似然译码，好于ＣｈａｓｅⅡ算法，且译码速度与ＣｈａｓｅⅡ算法接近。     

An Efficient Pseudocodeword Search Algorithm for Linear Programming Decoding of LDPC Codes

In linear programming (LP) decoding of a low-density parity-check (LDPC) code one minimizes a linear functional, with coefficients related to log-likelihood ratios, over a relaxation of the polytope spanned by the codewords. In order to quantify LP decoding it is important to study vertexes of the relaxed polytope, so-called pseudocodewords. We propose a technique to heuristcally create a list of pseudocodewords close to the zero codeword and their distances. Our pseudocodeword-search algorithm starts by randomly choosing configuration of the noise. The configuration is modified through a discrete number of steps. Each step consists of two substeps: one applies an LP decoder to the noise-configuration deriving a pseudocodeword, and then finds configuration of the noise equidistant from the pseudocodeword and the zero codeword. The resulting noise configuration is used as an entry for the next step. The iterations converge rapidly to a pseudocodeword neighboring the zero codeword. Repeated many times, this procedure is characterized by the distribution function of the pseudocodeword effective distance. The efficiency of the procedure is demonstrated on examples of the Tanner code and Margulis codes operating over an additive white Gaussian noise (AWGN) channel.     

Tightened Upper Bounds on the ML Decoding Error Probability of Binary Linear Block Codes

The performance of maximum-likelihood (ML) decoded binary linear block codes is addressed via the derivation of tightened upper bounds on their decoding error probability. The upper bounds on the block and bit error probabilities are valid for any memoryless, binary-input and output-symmetric communication channel, and their effectiveness is exemplified for various ensembles of turbo-like codes over the additive white Gaussian noise (AWGN) channel. An expurgation of the distance spectrum of binary linear block codes further tightens the resulting upper bounds     

Compensation Decoding of Space Time Frequency Block Codes

A novel compensation decoding scheme for a given space time frequency linear block code is presented, exploiting the simplicity of zero forcing equalization, and special characteristics of the preceding matrix. The proposed decoding procedure is relatively simple and straightforward in comparison to maximum likelihood decoding (MLD) and sphere decoding (SD). The bit-error-rate performance of the proposed scheme is better than zero forcing decoding and close to MLD and SD for low to medium signal-to-noise ratio range.     

Adaptive Methods for Linear Programming Decoding

Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we make a first step in studying this method, and show that by starting from a simple LP problem and adaptively adding the necessary constraints, the complexity of LP decoding can be significantly reduced. In particular, we observe that with adaptive LP decoding, the sizes of the LP problems that need to be solved become practically independent of the density of the parity-check matrix. We further show that adaptively adding extra constraints, such as constraints based on redundant parity checks, can provide large gains in the performance.      

Probabilistic Analysis of Linear Programming Decoding

We initiate the probabilistic analysis of linear programming (LP) decoding of low-density parity-check (LDPC) codes. Specifically, we show that for a random LDPC code ensemble, the linear programming decoder of Feldman succeeds in correcting a constant fraction of errors with high probability. The fraction of correctable errors guaranteed by our analysis surpasses previous nonasymptotic results for LDPC codes, and in particular, exceeds the best previous finite-length result on LP decoding by a factor greater than ten. This improvement stems in part from our analysis of probabilistic bit-flipping channels, as opposed to adversarial channels. At the core of our analysis is a novel combinatorial characterization of LP decoding success, based on the notion of a flow on the Tanner graph of the code. An interesting by-product of our analysis is to establish the existence of ldquoprobabilistic expansionrdquo in random bipartite graphs, in which one requires only that almost every (as opposed to every) set of a certain size expands, for sets much larger than in the classical worst case setting.     

A Novel Maximum Likelihood Decoding Algorithm for Orthogonal Space-Time Block Codes

In this letter, we propose a low complexity Maximum Likelihood (ML) decoding algorithm for orthogonal spacetime block codes (OSTBCs) based on the real-valued lattice representation and QR decomposition.We show that for a system with rate r = K/T, where K is the number of transmitted symbols per T time slots, the proposed algorithm decomposes the original complex-valued system into a parallel system represented by 2K real-valued components, thus allowing for a simple and independent detection of the real and imaginary parts of each complex transmitted symbol. We further show that for square L-QAM constellations, the proposed algorithm reduces the decoding computational complexity from /spl pdelta/(L) for conventional ML to /spl pdelta/(?L) without sacrificing the performance.     

A Kind of Quasi-Orthogonal Space-Time Block Codes and its Decoding Methods

1IntroductionSpace-Ti me Coding(STC)technology has been stud-ied extensively in recent years as a method to combatdetri mental effects in wireless fading channel and in-crease the transmission capacity in an open-loop way.Therein,a special class of space-…     

闭环模式的线性空时分组码

介绍了正交空时分组码的模型,自干扰,性能;并由此提出了一种高速率准正交空时分组码的闭环模式,保证MIMO系统获得较高的速率,同时减少由于正交性减弱而引起的性能下降.其中反馈的方法就是根据发射端能够获得部分信道状态信息而提出的,这种自适应模式的性能在瑞利衰落信道下通过仿真得到了验证.