Linear complexity and autocorrelation of a new class of binary generalized cyclotomic sequences of order two and length pqr

Cyclotomic sequences have good cryptographic properties and are closely related to difference sets.This paper proposes a new class of binary generalized cyclotomic sequences of order two and length pqr.Its linear complexity,minimal polynomial,and autocorrelation are investigated.The results show that these sequences have a large linear complexity when 2∈D1,which means they can resist the Berlekamp-Massey attack.Furthermore,the autocorrelation values are close to 0 with a probability of approximately 1?1/r.Therefore,when r is a big prime,the new sequence has a good autocorrelation.

Autocorrelation of Sequences Generated by Single Cycle T-Functions

Cryptographic properties of the single cycle T-function's output sequences are investigated.Bounds of autocorrelation functions of the kth coordinate sequence and bounds of state output sequence are calculated respectively.The Maximum Sidelobe Ratio(MSR) of the kth coordinate sequence and the MSR of state output sequence are given respectively.The bounds of autocorrelation functions show that the values of autocorrelation functions are large when shifts are small.Comparisons of the autocorrelations between the state output sequence and coordinate output sequence are illustrated.The autocorrelation properties demonstrate that T-functions have cryptographic weaknesses and the illustration result shows coordinate output sequences have better autocorrelation than that of state output sequences.

AUTOCORRELATIONS OF l-SEQUENCES WITH CERTAIN SHIFTS

In this paper, the autocorrelations of maximal period Feedback with Carry Shift Register sequences （l-sequences） are discussed. For an l-sequence a with connection integer q = p^e（e ≥ 2） and period T = p^t-1（p- 1）, and for any integer i, 1 ≤ i ≤ e/2, by calculating the number of certain sets, it is shown that the autocorrelation of a with shift τ= kT/2p^i is Ca（τ） =（-1）^k-1 T/p^2i-1, where 1 ≤ k ≤ 2p^i - 1, and gcd（k,2p^i） = 1. This result shows there do exist some shifts such that the autocorrelations of l-sequences are high although most autocorrelations are low. Such result also holds for the decimations of l-sequences.

A Hybrid Modified Sine Cosine Algorithm Using Inverse Filtering and Clipping Methods for Low Autocorrelation Binary Sequences

The essential purpose of radar is to detect a target of interest and provide information concerning the target’s location,motion,size,and other parameters.The knowledge about the pulse trains’properties shows that a class of signals is mainly well suited to digital processing of increasing practical importance.A low autocorrelation binary sequence(LABS)is a complex combinatorial problem.The main problems of LABS are low Merit Factor(MF)and shorter length sequences.Besides,the maximum possible MF equals 12.3248 as infinity length is unable to be achieved.Therefore,this study implemented two techniques to propose a new metaheuristic algorithm based on Hybrid Modified Sine Cosine Algorithm with Cuckoo Search Algorithm(HMSCACSA)using Inverse Filtering(IF)and clipping method to achieve better results.The proposed algorithms,LABS-IF and HMSCACSA-IF,achieved better results with two large MFs equal to 12.12 and 12.6678 for lengths 231 and 237,respectively,where the optimal solutions belong to the skew-symmetric sequences.The MF outperformed up to 24.335%and 2.708%against the state-of-the-art LABS heuristic algorithm,xLastovka,and Golay,respectively.These results indicated that the proposed algorithm’s simulation had quality solutions in terms of fast convergence curve with better optimal means,and standard deviation.

Almost perfect sequences based on cyclic difference sets

The perfect sequences are so ideal that all out-of-phase autocorrelation coefficients are zero, and if the sequences are used as the coding modulating signal for the phase-modulated radar, there will be no interference of side lobes theoretically. However, it has been proved that there are no binary perfect sequences of period 4 〈 n ≤ 12100. Hence, the almost perfect sequences with all out-of-phase autocorrelation coefficients as zero except one are of great practice in engineering. Currently, the cyclic difference set is one of most effective tools to analyze the binary sequences with perfect periodic autocorrelation function. In this article, two characteristic formulas corresponding to the autocorrelation and symmetric structure of almost perfect sequences are calculated respectively. All almost perfect sequences with period n, which is a multiple of 4, can be figured out by the two formulas. Several almost perfect sequences with different periods have been hunted by the program based on the two formulas and then applied to the simulation program and practical application for ionospheric sounding.

PERIODIC COMPLEMENTARY BINARY SEQUENCE PAIRS

A new set of binary sequences-Periodic Complementary Binary Sequence Pair (PCSP) is proposed. A new class of block design-Difference Family Pair (DFP) is also proposed.The relationship between PCSP and DFP, the properties and existing conditions of PCSP and the recursive constructions for PCSP are given.

Chaos game representation walk model for the protein sequences

A new chaos game representation of protein sequences based on the detailed hydrophobic-hydrophilic （HP） model has been proposed by Yu et al （Physica A 337（2004） 171）. A CGR-walk model is proposed based on the new CGR coordinates for the protein sequences from complete genomes in the present paper. The new CCR coordinates based on the detailed HP model are converted into a time series, and a long-memory ARFIMA（p, d, q） model is introduced into the protein sequence analysis. This model is applied to simulating real CCR-walk sequence data of twelve protein sequences. Remarkably long-range correlations are uncovered in the data and the results obtained from these models are reasonably consistent with those available from the ARFIMA（p, d, q） model.

LONG-RANGE CORRELATIONS IN DNA SEQUENCES USING TWO-DIMENSIONAL DNA WALKS

The characterization of long-range correlations and fractal properties of DNA sequences has proved to be adifficult though rewarding task mainly due to the mosaic character of DNA consisting of many patches of various lengthswith different nucleotide constitutions.In this paper we investigate statistical correlations among different positions in DNAsequences using the two-dimensional DNA walk.The root-mean-square fluctuation F(l)is described by a power law.Theautocorrelation function C(l),which is used to measure the linear dependence and periodicity,exists a power law ofC(l)-l^(-μ).We also calculate the mean-square distance<R^2(l)>along the DNA chain,and it may be expressed as<R^2(l)>-l^(?)with 2>γ>1.Our investigations can provide some insights into long-range correlations in DNA sequences.

CONSTRUCTIONOFACLASSOFPNSEQUENCESWITHPRIMENUMBERPERIODSOF4t＋1FORM

A class of new PN sequence with prime number periods of 4t +1 form (t is an integer)is constructed.The advantage of these PN sequencs over the m(M) sequence is their large number of alternative periods.They have good pseudo random characteristics demonstrated by the expression of periodic autocorrelation function found out in this paper.

Multi-Value Sequence Generated over Sub Extension Field and Its Properties

Pseudo-random sequences with long period, low correlation, high linear complexity, and uniform distribution of bit patterns are widely used in the field of information security and cryptography. This paper proposes an approach for generating a pseudo-random multi-value sequence (including a binary sequence) by utilizing a primitive polynomial, trace function, and k-th power residue symbol over the sub extension field. All our previous sequences are defined over the prime field, whereas, proposed sequence in this paper is defined over the sub extension field. Thus, it’s a new and innovative perception to consider the sub extension field during the sequence generation procedure. By considering the sub extension field, two notable outcomes are: proposed sequence holds higher linear complexity and more uniform distribution of bit patterns compared to our previous work which defined over the prime field. Additionally, other important properties of the proposed multi-value sequence such as period, autocorrelation, and cross-correlation are theoretically shown along with some experimental results.

两种改进型LPC特征参数对语音识别效果的影响

介绍了2种改进型的语音识别方法:单边自相关LPC系数法和线性预测误差法。这2种方法与传统的线性预测编码LPC法相比,其抗噪能力增强,即在强噪声环境下仍能达到较高的识别率。把这3种方法分别应用于端点检测和语音识别,用实验数据说明了2种改进型方法显著的抗噪性特点。

基于LPC的混响时间估计算法

准确计算混响时间需要知道房间的尺寸、墙壁的吸声系数等。经典的混响时间盲估计方法可以避免这些条件,但需要事先提供一个冲激信号。文章对经典算法进行了改进,提出了一种基于线性预测的混响时间盲估计算法。首先,将采集到的语音通过一个低阶的线性预测滤波器来获得线性预测残差信号;其次,计算残差信号的自相关,并选取合适的部分;最后,将选取的部分通过一个最大似然估计器,提取参数计算混响时间。文章还提出了一种改进的二分法来求解最大似然估计方程。实验证明,与经典算法相比,所提出算法估计的混响时间精度更高,且更具有实时性。

Autocorrelation Values of New Generalized Cyclotomic Sequences of Order Two and Length pq

Pseudo-random sequences are used extensively for their high speed and security level and less errors. As a branch, the cyclotomic sequences and the generalized ones are studied widely because of their simple mathematical structures and excellent pseudo-random properties. In 1998, Ding and Helleseth introduced a new generalized cyclotomy which includes the classical cyclotomy as a special case. In this paper, based on the generalized cyclotomy, new generalized cyclotomic sequences with order two and length pq are constructed. An equivalent definition of the sequences is deduced so that the autocorrelation values of these sequences can be determined conveniently. The construction contributes to the understanding of the periodic autocorrelation structure of cyclotomically-constructed binary sequences, and the autocorrelation function takes on only a few values.

Autocorrelation of two Legendre-Sidelnikov sequences

Sequences with nice pseudo-randomness play an important role in not only communication system but also cryptography system. Based on the Legendre-Sidelnikov sequence, a modified Legendre-Sidelnikov sequence was introduced. The exact value of the autocorrelation function was derived by strict computation. According to the values of the autocorrelation functions of the two Legendre-Sidelnikov sequences, it is proven that both of them have perfect pseudo-randomness. Furthermore, a detailed comparison between autocorrelation functions of the two Legendre-Sidelnikov sequences was deduced. It indicates that no matter which parameters are chosen, the modified sequence has pseudo-randomness as good as the primitive sequence, which is of great significance for applications.

基于FPGA的LPC总线转多路SPI总线设计

该文介绍了LPC和SPI总线的应用场景,以及总线协议的工作原理。通过对工作原理的研究完成了LPC总线与多路SPI总线转换方案设计,提出了基于FPGA的具体实现方法,具有逻辑清晰、灵活高效和高扩展性特点,能够实现LPC总线对SPI总线设备的多路识别和通信。最后通过仿真实验,得到了I/O读写模式下写和读的时序图,验证了设计的可靠和有效性。

两类具有低自相关和大线性复杂度的4p周期二元序列

具有良好自相关性质和大线性复杂度的二元序列设计对于通信系统和流密码的各种应用非常重要.本文从Hall六次剩余序列和它们的修改版本中选取4条合适的序列作为基序列,利用交织技术构造了两类周期为4p的二元序列,并且完全确定了这两类序列的自相关和线性复杂度.研究结果表明这两类序列既具有低自相关性质又具有非常大的线性复杂度.

具有优异汉明相关特性的混沌跳频序列构造方法

跳频通信具有码分多址、频带共享、抗干扰和抗截获的能力,在无线通信系统中得到了广泛的应用。目前基于混沌方法构造的跳频序列大多具有较高的线性复杂度,所得到的跳频序列虽然具有良好的随机性,但是其汉明相关性还不够。在选取具有优异汉明相关特性的m序列的基础上,结合混沌序列,利用笛卡尔积构造得到了具有优异汉明自相关性的跳频序列。该跳频序列具备与混沌序列一致的线性复杂度,而且可以保证其周期不小于m序列的周期,汉明自相关值不超过m序列的汉明自相关值。

一类折叠次数无限的混沌自映射及其应用

提出了一类在有限区域 [- 1 ,1 ]范围内折叠次数为无限的一维迭代混沌自映射 .分析了该映射的混沌产生机制 ,计算出的 Lyapunov指数表明 ,该混沌映射比一般的有限折叠次数迭代混沌自映射具有更好的混沌特性 .利用该映射生成 CDMA混沌扩频序列 ,能获得比工程实用中常见的 Gold序列性能更加优良的自相关与互相关特性 。

小波分层阈值降噪法及其在发动机振动信号分析中的应用

通过对小波消噪原理的分析及常用阈值规则的降噪性能对比,提出了基于小波细节系数自相关性分析的分层阈值降噪法,描述了根据有用信号最小频率成分确定最大分解层数的方法,给出了分层阈值降噪法的步骤,并对模拟的含噪振动信号进行了试验研究,结果表明,该方法具有较好的降噪效果,尤其适合于强噪声背景下弱信号的恢复,有利于较高频率有用信号的提取。最后,对小波分层阈值降噪法在发动机振动信号分析中的实际应用进行了研究,研究证明,该方法可以有效地抑制背景噪声,提取有用状态信息,为发动机振动信号预处理提供了一种切实可行的方法。

清浊音判决算法在语言康复训练中的应用

利用LPC求残差系数,然后对残差系统求自相关,再判断自相关的参数序列是否具有周期性而实现清浊音的判决。利用此算法结合计算机的智能诊断实现了一个应用系统,此应用系统能够让语言障碍患者进行清浊音康复训练,在临床应用中取得了良好的效果。