基于二次乘法特征的射影线性码

基于有限域上的二次乘法特征构造了两类线性码，精确计算出了它们的参数和重量分布.结果表明，第一类线性码是射影三重码，且对偶码关于球填充界几乎最优；第二类线性码是射影二重码，且对偶码关于球填充界几乎最优.此外，本文还得到了一些自正交码和极小码，它们可分别用于构造量子码和安全高效访问结构上的密钥共享方案.     

准循环码和七个新的二元线性码

本文利用一类准循环码的结构进行计算机搜索，再加上通常的码的变换，共得到了七个新的二元线性码，它们都改进了文「１」中二元线性码极小距离的下界，其中有三个是最优的。     

等距码的几点注记

设Ｑ（ｎ，ｄ）为码长为ｎ，任意两个不同码字之间的Ｈａｍｍｉｎｇ距离为ｄ的二元等距码所能达到的最大码字数，本文确定了Ｑ（ｎ，ｄ）的一些精确值，并且给出了最优等距码的一些性质。     

几类near MDS码和最优局部修复码的构造

局部修复码是一种通过局部修复提高存储节点修复效率的重要编码方法,在分布式存储和云存储中有重要应用.本文首先构造了几类维数为4或5的near MDS (near Maximum Distance Separable)码,精确计算出了它们的参数和重量分布.特别地,得到了一些参数相同但重量分布不同的near MDS码.此外,通过确定near MDS码的局部度,得到了几类距离最优和维数最优的局部修复码.这些局部修复码的参数和文献中已知最优局部修复码的参数不同.     

空时格码迹准则的改进

本文研究空时格码迹设计准则的改进问题.原迹准则的不足在于仅考虑了码的最小迹,故不能有效的选取最优码.针对这一不足,本文首先提出了以迹分布作为衡量码性能主要依据的思路.然而迹分布仍不能完全决定码的性能,于是文中导出了一个新的错误概率上界,并在此基础上又提出了以特征值和方/方和比分布来补充和完善迹分布的思路.最后综合以上两个分布,本文给出了一个改进的空时格码设计准则,并根据这一准则找到了一些新码,仿真结果表明这些新码的性能为目前已知码中最优的.     

分布式空时编码

利用空间维度，结构简单的多节点相互协助形成的协作分集系统正成为MIMO之后又一热点。分布式空时码也在空时码的相对成熟后得到了很大发展。通过中断概率的上下界给出理论分布式空时码所达到的性能后，本文详细的阐述了最近三种分布式空时码的构造方法，达到最优的条件，运用的场合以及分集度分析。最后，本文介绍了一种简单的不采用空时编码获得满分集的方法以及它的问题。     

之型码和级联之型码

本文介绍了一种新型的纠错码，称之为“之型码”。之型码可以形成非常简捷的软输入/软输出译码规则，我们在Max-Log-MAP(MLM)译码方法的基础上提出了一种译码规则，这一译码规则的计算复杂度为每次迭代计算单位信息比特大约需要20次加法运算操作。在仿真实验中，我们用最优译码器和更简捷的次最优译码器进行译码时，其性能在误比特率为10^-5处分别距香农理论极限仅0.9dB和1.4dBH。此外，上述码字与2维turbo码相比具有更低的误码基底值（error floor）。     

一类p元最优线性码和低相关性线性序列的构造

在信息理论中,最优线性码具有很强的纠错能力、低相关性线性序列在密码系统和CDMA通信系统中得到了广泛应用.因此构造最优线性码和构造低相关性线性序列具有重要的研究价值.记R=Fp+uFp,这里的p为奇素数.本文首先通过迹映射构造出环R上的一类新的线性码,然后将这类新的线性码的删余码通过Gray映射得到了域Fp上一类最优码.同时,通过迹映射构造出环R上的一类线性循环码,将这类线性循环码视为线性周期序列并通过广义Nechaev-Gray映射得到了域Fp上一类低相关线性周期序列.     

基于遗传算法的矢量量化

本文提出了一种基于遗传算法的矢量量化方法。矢量量经码书设计本质是搜索训练矢量的最佳分类。遗传算法有卓越的全局优化搜索能力，易搜索到全局最优的矢量分类，形成高度优化的码书，可克服传统方法局部优化的缺陷。该方法不依赖初始条件、鲁棒性好、结构规则、并行性高。     

OFDM系统下LDPC码的性能仿真

通过对LDPC码在不同调制方式下译码算法的分析，把高阶调制下的和积译码算法应用于LDPC—OFDM系统，系统中LDPC码采用目前性能最优的PEG随机构造生成，并与Turbo—OFDM系统进行比较，仿真结果表明短码长LDPC码在高码率高信噪比的情况下性能优于Turbo码。     

COMPUTER SIMULATION FOR AN ULTRA-LOW RANGE SIDELOBE PULSE COMPRESSION SCHEME

A canceling range sidelobes scheme has been suggested by Yang Guangzheng, et al.,(1997) this technology is based on the fact that all sidelobe of group correlation function of ideal sets are zero. At first, this paper gives the best ideal sets (i. e. the best biphase code sets whose maximal sidelobe not more than 2) for all code length N≤12, which have been obtained from binary sequences by means of the best codes sieving method suggested by Yang Guangzheng, et al.(1997) Computer simulation for group correlation property of best ideal sets for code length N=12 on various conditions is made. Simulation result shows that the sidelobe level of best ideal set with no weighting is zero, under condition of zero-Doppler shift and has ultra-low sidelobe on Doppler up to 5kHz with no weighting and whose tolerance of phase and amplitude distortion is bigger too.     

A (48, 31, 8) linear code (Corresp.)

In this paper we construct a linear code having length 48, minimum distance 8, and containing2^{31}codewords. This code is obtained by augmenting a (48,22,8) linear code with2^9- 1 cosets so that the minimum distance is not reduced. The (48,22,8) code used is the direct product of a (16,11,4) extended Hamming code and a (3,2,2) single-parity-check code. The new code has twice as many codewords as the best linear or nonlinear code previously known.     

Choice of Prefix in Self-Synchronizing Codes

In this correspondence a special prefix code with stuffing bits is described and the sequences that are more suitable as prefixes, called valid sequences, are determined by means of a condition they must satisfy. The best prefix length as a function of the total number of bits in the code is then evaluated.     

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.     

Any code of which we cannot think is good

A central paradox of coding theory concerns the existence and construction of the best codes. Virtually every linear code is good, in the sense that it meets the Gilbert-Varshamov bound on distance versus redundancy. Despite the sophisticated constructions for codes derived over the years, however, no one has succeeded in demonstrating a constructive procedure that yields such codes over arbitrary symbol fields. Using the theory of Kolmogorov complexity, it is shown that this statement holds true in a rigorous mathematical sense: any linear code that is truly random, in the sense that there is no concise way of specifying the code, is good. Furthermore, random selection of a code that does contain some constructive pattern results, with probability bounded away from zero, in a code that does not meet the Gilbert-Varshamov bound regardless of the block length of the code. In contrast to the situation for linear codes, it is shown that there are effectively random nonlinear codes which have no guarantee on distance. In addition, it is shown that the techniques of Kolmogorov complexity can be used to derive typical properties of classes of codes in a novel way     

Enhanced Secure Error Correction Code Schemes in Time Reversal UWB Systems

In this paper, secure channel coding schemes based on turbo codes are suggested for time reversal ultra wideband (TR-UWB) systems. Turbo code has the capability of error correction near Shannon’s limit. Adding security to turbo code is an attractive idea since it could reduce the overall processing cost of providing secure coded data and enjoys the advantages of high-speed encryption and decryption with high security, smaller encoder and decoder size and greater efficiency. The proposed turbo code schemes are labeled as follows: secure puncturing rate, secure frame length, and secure interleaving. Using these scenarios, secure turbo code is defined in a way that the redundant information used for error correction is not pre-determined by the nature of the error correction part of the algorithm but it can be chosen arbitrarily out of the whole set of possible strings. The lower bound of bit error probability for secure turbo code schemes in AWGN and TR-UWB systems are evaluated. Analytical and simulation results show secure turbo code performance is very satisfying. Various crypto-analytical attacks are investigated against these schemes. Based on this analysis, secure turbo code structures changed during the encryption procedure to increase the complexity of linear and differential cryptanalysis. It is seen that the performance of conventional turbo code and random frame length with Poisson distribution are the same. Comparing these schemes shows, secure interleaving approach has the best performance and secure puncturing rate the worst, but the latter provides the most security. The enhanced security of UWB, due to rich multipath nature of UWB channel, could be exploited. Due to space-time focusing property of time reversal UWB, there is an environmental confidentiality (or spatial security), which is additional security for secure turbo code in this system. Using secure turbo code, it is possible to increase the transmission range of UWB systems.     

带禁止符号的算术码序列译码算法

如何有效检测错误以及如何构造编码树型结构是算术码抗误码性能研究的两个关键性问题。文章利用多禁止符号实现快速、高效检错,并结合删减编码树型结构分支点的序列译码算法,在降低序列译码复杂度的同时提高了算术码的抗误码性能。仿真结果表明,在同样误包率的条件下,多禁止符号的抗误码性能优于单禁止符号0．5dB。而且在数据包长固定的条件下,禁止符号冗余度的选择和序列译码堆栈空间大小密切相关,联合优化后可以达到性能最优。     

Performance of coding-spreading tradeoff in DS-CDMA systems using RCPT and RCPC codes

The use of rate-compatible punctured turbo and rate-compatible punctured convolutional (RCPT/RCPC) codes as channel codes in a direct-sequence code-division multiple-access system where the system bandwidth expansion is fixed is investigated. The best RCPC and RCPT code rate in terms of maximizing the system spectral efficiency and minimizing the optimal power allocation where the receiver is either a matched filter (MF) or a minimum mean-square error (MMSE) device is assessed. It is shown that for the MF receiver, the coding-spreading tradeoff favors a code-rate reduction. In the case of the MMSE receiver, when the E/sub b//N/sub 0/ value and the system load are increased, the best code rate also increases. By examining the slope of the performance curves, it is deduced that, under similar operating conditions, the best code rate of the RCPT codes is lower than that of the RCPC codes. Also, the best code rate for a Rayleigh fading channel is lower than that for an additive white Gaussian noise channel.     

Errors and erasures decoding of BCH and Reed-Solomon codes for reduced M-ary orthogonal signaling

The paper presents a comparison of communication systems using different signal constellation sizes and Reed-Solomon or Bose-Chaudhuri-Hocquengem codes with different rates so that the overall required bandwidth is the same for each system. In these comparisons, the channel symbol size is smaller than the code symbol size, so that a code symbol contains parts of multiple channel symbols. Thus, the normal assumption of independent code symbols does not apply. Instead, consideration must be taken to obtain the best arrangement of channel symbols in each code symbol. Analytical expressions are developed to compare the bit error probability performance of comparable systems, based on individual codewords using errors-only decoding and errors and erasures decoding with transmission over a Rayleigh fading channel.