低密度纠删码稳定收敛条件的证明

基于数学分析中著名的不动点原理,对于低密度纠删码本文证明了其删除错误译码算法稳定收敛的一充分条件.而且指出此条件优于现有的稳定收敛条件.最后对给定的度分布对证明了此译码算法能成功译码时可接受的最大损失δ的几个上界.     

方阵码恢复可抹信号的性能评价

在一些通信系统中,接收机主要面向可抹信号。可抹信号可以通过方阵码译码恢复。传统上是通过最小码间距来评价译码性能。从方阵码中可抹信号的空间分布结构入手,能够推导出方阵码迭代译码后可抹信号率上界的新算法。仿真显示这个上界比基于最小码间距分析的上界更紧,对性能的评价更为精确。     

无线传输中短码长喷泉码的度分布优化算法

数字喷泉码是针对大规模网络数据分发而提出的一种新的信道编码方式。度分布是决定数字喷泉码译码性能的关键因素。为提高译码性能,针对应用于无线信道的喷泉码提出了一种度分布优化的算法。首先,根据理想孤子分布和鲁棒孤子分布产生度值序列,然后将该度值序列截短,在此基础上根据优化算法求解该序列中每个度值的最优概率,最后得到优化的度分布。仿真结果表明,本算法产生的度分布进行编译码产生的误码率低于鲁棒孤子分布和固定度分布,提高了译码性能。     

LT码的增强型BP译码算法

传统的LT码采用的BP译码算法,当不存在度1编码分组时会导致BP译码算法失败,不能继续译码.为了提高译码的成功率,分析了剩余编码分组的结构,提出LT码的再次译码算法(Again Belief Propagation decoding algorithm,ABP).算法主要思想是BP译码失败后,查找满足条件的可译结构,继续译码,直到译码成功或再次失败,如果失败重复上面步骤直到译码成功或可译结构不存在,从理论上分析了可译结构存在的概率.仿真结果显示译码成功率得到提高.     

基于IBED和仿生算法的LT码度分布设计

度分布是影响Luby变换（Luby transform,LT）码性能优劣的关键因素,为了得到更优的度分布,提出一种基于改进的二进制指数分布（improved binary exponential distribution,IBED）和仿生算法的LT码度分布设计方案.采用IBED度分布进行LT编码,初始译码成功率可高达90%以上,但随着译码开销增大,译码成功率上升速度减缓,而此时鲁棒孤子分布（robust soliton distribution,RSD）的译码性能表现更佳.为了将IBED和RSD的优点有机结合,利用人工鱼群算法（artificial fish swarm algorithm,AFSA）在两种度分布间寻优,基于期望可译集构建该算法的目标函数,通过最大化目标值得到更优的度分布.仿真结果表明,与类似方法及传统的RSD相比,采用新度分布进行LT编码可明显降低译码开销,并节约编译码耗时.     

关于纠删码的研究与进展

该文简述了几类纠删码的纠删原理,系统地综合分析了各类纠删码的优缺点及其相互区别与联系,证明了若选取MDS(Maximal Distance Separable)码作为纠删码,只要接收者接收到源数据个数的数据,就能恢复原来的源数据。分析结果表明:复损码以及旋风(Tornado)码不仅能以线性时间可编码和可成功地译码,而且能以任意接近删除信道容量的速率进行传输,最后指出了目前复损码的研究中需要解决的一些问题,这些分析和结论为进一步研究纠删码提供了理论基础和新的思路。     

一种改进的基于部分信息喷泉码度分布设计

与传统的喷泉码相比,基于反馈信息的喷泉码可以有效降低译码开销,其编码所采用度分布则是喷泉码设计的关键,本文提出一种适用于反馈喷泉码的基于部分信息度分布构造方法.该方法首先提出具有较小译码开销的最佳单项式度分布函数,并将其与传统的SRSD度分布相结合,然后通过参数调整可以获得修正后的ISRSD度分布函数.仿真结果表明在已知部分信息的喷泉码中,与传统的SRSD度分布函数相比,采用ISRSD度分布函数进行编码使其性能得到明显的提高.     

基于置信传播译码的DRA码设计

该文通过重复器、组合器、交织器的联合优化,设计了一种没有小环的双重复累积码(DRA码);基于EXIT图优化设计了该码的度分布。研究结果显示,这类DRA码的度分布灵活;当采用置信传播译码时,错误平层低。     

基于度分布合并和可译集优化的LT码度分布设计方案

喷泉码的度分布对喷泉码的编译码性能有着十分重要的影响.目前常用的度分布在源数据码长较长时具有较好的性能,但在码长较短时,性能有明显下降.本文给出一种LT码度分布的构造方法.该方法先对二进制度分布进行调整,然后将其与鲁棒孤子度分布进行有机结合,再通过优化可译集合值来进一步优化度分布函数,得到一种当源数据为短码长时也有较好性能的度分布,即修正二进制-鲁棒孤子度分布.仿真结果证明,采用这种度分布对源数据进行LT编码时,相比较二进制度分布和鲁棒孤子度分布,其译码性能得到了明显提高,并且码长越短,性能提高越明显.     

基于卢比变换码的分解重组编码算法

LT(卢比变换)码是第一个能够实际应用的数字喷泉码。尽管采用BP(置信)译码算法的LT码的编译码复杂度已接近线性,但依然会增加较大的时延。文章提出了一种DRE(分解重组编码)算法,对所有信息包分解后重新组合,分成多组并行编码,有效地降低了编码时间和译码的操作数,减少了数据传输时延。该编码方法可适用于不同度分布函数。仿真结果表明,当信息包数量K=1 000和2 000时,采用同样的度分布可以达到NRE(非重复编码)的性能,并能够减少约75%的编码时间和大量的译码操作数。     

DC-free error-correcting codes based on convolutional codes

A new construction of direct current (DC)-free error-correcting codes based on convolutional codes is proposed. The new code is constructed by selecting a proper subcode from a convolutional code composed of two different component codes. The encoder employs a Viterbi algorithm as the codeword selector so that the selected code sequences satisfy the DC constraint. A lower bound on the free distance of such codes is proposed, and a procedure for obtaining this bound is presented. A sufficient condition for these codes to have a bounded running digital sum (RDS) is proposed. Under the assumption of a simplified codeword selection algorithm, we present an upper bound on the maximum absolute value of the RDS and derive the sum variance for a given code. A new construction of standard DC-free codes, i.e., DC-free codes without error-correcting capability, is also proposed. These codes have the property that the decoder can be implemented by simple symbol-by-symbol hard decisions. Finally, under the new construction, we propose several codes that are suitable for the systems that require small sum variance and good error-correction capability     

Performance of low-density parity-check codes with linear minimum distance

This correspondence studies the performance of the iterative decoding of low-density parity-check (LDPC) code ensembles that have linear typical minimum distance and stopping set size. We first obtain a lower bound on the achievable rates of these ensembles over memoryless binary-input output-symmetric channels. We improve this bound for the binary erasure channel. We also introduce a method to construct the codes meeting the lower bound for the binary erasure channel. Then, we give upper bounds on the rate of LDPC codes with linear minimum distance when their right degree distribution is fixed. We compare these bounds to the previously derived upper bounds on the rate when there is no restriction on the code ensemble.     

Optical orthogonal codes with large crosscorrelation and their performance bound for asynchronous optical CDMA systems

Optical orthogonal codes (OOCs) are commonly used as signature codes for optical code-division multiple-access (OCDMA) communication systems. Many OOCs have been proposed and investigated. Asynchronous OCDMA systems using conventional OOCs have a very limited number of subscribers and few simultaneous users. Recently, we reported a new code family with large code size by relaxing the crosscorrelation constraint to 2. In this paper, by further loosening the crosscorrelation constraint, we adopt the random greedy algorithm to construct a code family which has larger code size and more simultaneous users. We also derive an upper bound of the number of simultaneous users for a given code length, code weight, and bit error rate. The study shows that it is possible to have codes approaching this bound.     

低密度奇偶校验码码字构造的消环算法

低密度奇偶校验码(LDPC)的性能取决于多种因素,包括度分布对、码字的长度以及环的分布。环的存在会影响LDPC码的译码门限和误码平层,尤其是长度比较小的环对LDPC码的性能影响很大。因此,有必要在构造LDPC码时消去长度比较小的环。文中提供了一种有效的消环算法,降低了LDPC码的误码平层。     

Evaluation of transfer functions for punctured turbo codes

A modified algorithm for evaluating transfer functions of turbo codes with punctured systematic bits is presented. The obtained transfer function leads to a more accurate estimation of the weight distribution of the code. Consequently, a tighter upper bound on the bit error rate performance of the code is obtained     

重量分布式约束的LDPC码性能研究

本文对"重量分布式约束的码集合内码性能"这一命题进行了初步研究,分别得到了码集合性能的上限和下限,本文给出了性能下限码的Fill-Shift构造方法,而且由LDPC码校验矩阵不变性可以对LDPC码的校验矩阵作必要的初等变换,这样可以在保持码性能不变的前提下降低编码复杂度和实现系统编码;此外,还可以利用该性质加强对重要信息符号的差错保护.     

An upper bound on the minimum distance of a convolutional code

An upper bound on the minimum distance of a linear convolutional code is given which reduces to the Plotkin bound for the block code case. It is shown that most linear convolutional codes have a minimum distance strictly less than their average distance. A table of the bound for several rates is given for binary codes as well as a comparison with the known optimum values for codes of block length2.     

Soft-decision list decoding of hermitian codes

This paper proposes the first complete soft-decision list decoding algorithm for Hermitian codes based on the Koetter- Vardy's Reed-Solomon code decoding algorithm. For Hermitian codes, interpolation processes trivariate polynomials which are defined over the pole basis of a Hermitian curve. In this paper, the interpolated zero condition of a trivariate polynomial with respect to a multiplicity matrix M is redefined followed by a proof of the validity of the soft-decision scheme. This paper also introduces a new stopping criterion for the algorithm that tranforms the reliability matrix ? to the multiplicity matrix M. Geometric characterisation of the trivariate monomial decoding region is investigated, resulting in an asymptotic optimal performance bound for the soft-decision decoder. By defining the weighted degree upper bound of the interpolated polynomial, two complexity reducing modifications are introduced for the soft-decision scheme: elimination of unnecessary interpolated polynomials and pre-calculation of the coefficients that relate the pole basis monomials to the zero basis functions of a Hermitian curve. Our simulation results and analyses show that soft-decision list decoding of Hermitian code can outperform Koetter-Vardy decoding of Reed-Solomon code which is defined in a larger finite field, but with less decoding complexity.     

An upper bound for codes in a two-access binary erasure channel (Corresp.)

A method for determining an upper bound for the size of a code for a two-access binary erasure channel is presented. For uniquely decodable codes, this bound gives a combinatorial proof of a result by Liao. Examples of the bound are given for codes with minimum distance 4.