二元DNA Hamming码的设计及分析

DNA计算作为一种新的计算模式,有着强大的计算能力。实验表明,有效的编码可以提高DNA计算的可靠性,从而保证DNA计算的成功率。二元Hamming码是一类达到Hamming界的好码,也是仅有的两类完全码中的一类。文中基于纠错码编码理论给出了二元DNA Hamming码的设计过程,并进一步分析了所设计的二元DNA Hamming码的性质及其优点。     

DNA计算编码研究及其算法

编码问题仍是目前DNA计算中的重点和难点之一,实践证明通过有效的编码设计能够提高DNA计算过程中可靠性.本文介绍了约束条件的生物学特性,分析了约束条件与编码数量的关系,并给出编码的计数公式.文中设计了一种基于三字母表{A,T,C}的线性码的编码构造算法,并对运行结果进行了比较分析,同时分析了结果编码的热力学性质.最后指出DNA计算编码存在的问题及下一步的研究方向.     

不同脉冲编码调制的BOTDA系统性能分析与比较

研究了基于脉冲编码调制的布里渊光时域分析(BOTDA)系统原理,该系统向传感光纤注入经脉冲编码调制后的光脉冲序列,在接收端用数据处理程序恢复系统的单脉冲响应,从而提高BOTDA系统的信噪比、温度和应变分辨率.理论研究了BOTDA系统中Simplex码、Golay码和CCPONS码的编码和解码原理;利用Matlab仿真研究了不同脉冲编码调制的BOTDA系统的时域输出信号,并对比分析了三种编码对系统信噪比的改善情况,结果表明采用脉冲编码技术可使BOTDA系统性能得到有效提升,CCPONS码调制时可获得最佳系统性能,Simplex码次之.     

基于DNA域编码的余三码四位减法器的设计

DNA分子逻辑电路的设计是DNA计算领域的重要研究方向。该文针对当前双轨分子逻辑电路复杂度高、响应时间慢的问题,提出一种基于域编码策略的DNA逻辑电路设计的新方法。该文设计了“多输入1输出”逻辑运算模块,构建了扇出门和放大器,并利用所构建的电路模块搭建了4位平方根分子逻辑电路,与经典的双轨策略下的4位平方根电路相比,反应物的数量由双轨的130种降低为61种,系统响应时间缩减为双轨的1/24,大大简化了电路的复杂度,提高了系统的响应速度,进一步验证了域编码策略在分子逻辑电路设计中的有效性。为了深度解析基于域编码策略的大规模复杂分子逻辑电路的设计思想,该文构造了“余三码四位减法器”,为设计大规模功能性DNA逻辑电路提供了更多的解决方案。     

DNA编码技术探讨

文中研究了DNA编码的一般约束条件-编码距离的各种情况,找出了其中的某些等价计算,对任意两个编码序列的编码距离提出了最简化的计算方法,降低了基于汉明距离约束的计算复杂度。同时,文中还分析了Adleman哈密尔顿路径实验中采用的编码性能,提出了全新的性能更好的编码,并设计了生物验证实验进行验证。     

DNA编码的计算机筛选策略研究

1994年,Adleman提出了使用DNA分子进行计算的模型并通过实验得到了验证,昭示了这一新方法在大规模并行计算和数据存储中使用的广阔前景。然而,至今仍有很多影响其投入实际使用的关键问题未能得到很好地解决,DNA编码问题便是其中之一。文中分析了DNA编码中存在的限制条件,提出了使用计算机筛选DNA编码的思路,并使用计算机筛选出的DNA编码开展了分子生物学实验,旨在提供计算机快速有效筛选DNA编码的方法。     

一种扩展戈莱码的编译码方法

在MIL-STD-188-141A协议中采用的是扩展戈莱(Golay)码。它是[23,12]戈莱(Golay)码演变而来的。提出了一种在[23,12]Golay生成矩阵的基础上得到扩展戈莱码生成矩阵的方法,并对扩展戈莱码的译码方法进行了讨论,最后用MATLAB对编译码算法进行了仿真。     

基于Golay脉冲编码技术的相干激光雷达仿真研究

针对相干激光雷达远场回波信号信噪比低,提取困难的问题,提出了脉冲编码技术,以改善系统信噪比,增大雷达探测距离。研究了相干激光雷达系统中Golay码的编码和解码原理,理论分析了采用脉冲编码技术对系统信噪比的提升效果。基于大气分层模型仿真生成了相干激光雷达时域回波信号。基于Golay码解码原理得到了脉冲编码系统的风速结果,仿真结果表明,时间分辨率为1s,距离分辨率为60m的情况下,使用Golay编码脉冲作为相干激光雷达的探测脉冲,在0~5.3km范围,风速误差小于3m·s~(-1)。在相同的测量时间内,相比于传统脉冲相干激光雷达,基于脉冲编码技术的相干激光雷达将探测距离提高了2.5km,提高了远场弱信号的信噪比。     

OFDM系统中峰平功率比减小技术的研究

主要对减小OFDM系统中的峰值平均值功率比(PAPR)问题进行了研究。利用Golay互补序列和Reed-Muller码的关系,研究了一种把输入信息序列编成Golay互补序列的分组编码算法,并利用该编码算法对一个16子载波的OFDM系统的PAPR特性进行仿真。理论研究和仿真结果均表明,采用该编码方案后的OFDM信号的PAPR不超过3dB。     

降低16QAM-OFDM信号峰均功率比的方法研究

针对0FDM峰均功率比(PAPR)问题,提出利用Golay互补序列(GCS)降低16QAM-0FDM信号PAPR的方法,分析了其PAPR最大值、16QAM序列集合大小以及编码率,讨论了编译码算法和纠错能力.研究结果表明,这些降低PAPR的方法在系统设计有不同要求时具有不同先决应用条件.     

A property of decomposable Golay codes which greatly simplifies sidelobe calculation

Pure-sense complementary sequences are an important class of codes that were invented by Golay. With but two non-trivial exceptions, Golay codes of all known lengths are, or can be, made to be decomposable; that is, they can be considered to be formed from the apposition of two equal-length subcodes. Hence the technique in this letter applies to Golay codes of most known lengths. The value of the property is that it reduces the labor of computation of the autocorrelation function sidelobes of the Golay codes by a factor of at least two. Furthermore, it is applicable to either marine or manual calculation. It also provides another way of analyzing auto-correlation functions in general.     

New simple encoder and trellis decoder for Golay codes

New simple encoding and trellis decoding techniques for Golay codes, based on generalised array codes (GAGs) are proposed. The techniques allow the design of both (23,12,7) Golay and (24,12,8) extended Golay codes with minimal trellises. It is shown that these trellises differ only in the last trellis depth with different labelling digits.<>     

On the computation of the probability of post-decoding error events for block codes (Corresp.)

The computation of the probability of certain post-decoding error events is formulated for block codes whose weight distributions are known. A bounded-distance decoder for group codes is assumed. Numerical examples included show post-decoding character error rates for the Golay code and for some Reed-Solomon codes and the distribution of post-decoding errors for the same Reed-Solomon codes. An extension to errors and erasures decoding is also given.     

Multiphase Complementary Codes

A new class of complementary codes, similar to the complementary series of Golay but having multiphase elements, have been found to exist with specific complementary aperiodic complex autocorrelation functions. These new codes, called multiphase complementary codes, form a class of generalized complementary codes, of which the Golay complementary series can be considered to be a particular biphase subclass. Unlike Golay pairs, kernels of the new codes exist for odd length and can be synthesized. These new codes, like Golay pairs, are characterized by mathematical symmetries that may not be initially obvious because of apparent disorder. Multiphase complementary codes can be recursively expanded and used to form orthogonal or complementary sets of sequences. These complementary sets are not constrained to have even length or even cardinality. In addition, certain generalized Barker codes can also be utilized to form complementary sets with unique properties.     

Linear codes with Pless structures

Extended Golay codes possess certain two-level structures which are important for decoding the codes. However, these ideal structures are not limited to Golay codes. Here, the structures are generalised to other linear codes. Among which are a binary (20. 9, 7) code, a binary (32, 16, 8) code, a binary (40, 20, 8) code and a ternary (18, 9, 6) code. Similar to the Golay codes, there are also efficient decoding algorithms for these codes, which are sufficiently simple to enable decoding the derived codes by hand calculations     

Decoding the Golay codes

We introduce exceptionally simple decoding algorithms for the two extended Golay codes. The algorithms are based on recent methods of Conway and Curtis of finding the unique blocks containing five points in either the(5,8,24)Steiner system or the(5,6,12)Steiner system. These decoding methods are simple enough to enable decoding extended Golay codes by hand. Both of the methods involve relations between the extended Golay codes and other self-dual codes. Proofs are given explaining these relationships and why the decoding methods work. The decoding algorithms are explained and illustrated with many examples.[3, chap.12]has facts about the Mathieu group and some details about decoding the Golay codes.     

基于神经网络的（23,12）Golay码译码新算法

对Ｈｏｐｆｉｅｌｄ神经网络（Ｈ．Ｎ．）在纠错编译码技术中的具体应用进行了研究，分析指出了该网络与循环码，尤其是Ｇｏｌａｙ码的关系，提出了一种采用高阶互连网络实现循环码最大似然译码的方法，并且实现了一套有效的算法，非常完满地解决了（２３，１２）Ｇｏｌａｙ码的完全译码。最后指明了硬件实现的思路。     

The `stretched'-Golay and other codes for high-SNR finite-delayquantization of the Gaussian source at 1/2 bit per sample

Error-correcting codes are considered as codebooks for high-performance vector quantization (VQ) of the IID Gaussian source at fractional bit rate. A family of good rate-one-half codes is introduced: the stretched Golay codes. The performance of these codes is compared to other good block codes, trellis-coded quantization, and other techniques. The stretched Golay codes are shown to outperform previously published results for block lengths 32, 40, 56, and 64. The good performance, together with fast decoding make these techniques attractive for applications such as low-bit-rate coding of speech