Number theoretic transforms over the golden section quadratic field

A new number theoretic transform (NTT) over the real quadratic field Q(√5) is suggested and analyzed. Conventional NTTs are used for fast convolution of integer sequences. A new approach for computing number theoretic transforms (NTTs) is proposed, allowing real signals to be processed as well. The method is based on a Diophantine approximation of the input real signal before the NTT. The choice of the three parameters characterizing any NTT-modulus, transform length, and primitive element-is discussed in detail. From a practical point of view, the suggested NTTs offer attractive combinations of these parameters. Much care has been exercised to reduce the computational complexity. The practical usefulness of an irrational number system is demonstrated. Extensions and open problems are discussed     

On the parameterization of positive real sequences and MA parameterestimation

An algorithm for moving average (MA) parameter estimation was proposed by Stoica et al. (see ibid. vol.48, p.1999-2012, 2000). Its key step (covariance fitting) is a semidefinite programming (SDP) problem with two convex constraints: one reflecting the real positiveness of the desired covariance sequence and the other having a second-order cone form. We analyze two parameterizations of a positive real sequence and show that there is a one-to-one correspondence between them. We also show that the dual of the covariance fitting problem has a significantly smaller number of variables and, thus, a much reduced computational complexity. We discuss in detail the formulations that are best suited for the currently available semidefinite quadratic programming packages. Experimental results show that the execution times of the newly proposed algorithms scale well with the MA order, which are therefore convenient for large-order MA signals     

伪码测距中码跟踪环的FPGA实现

码跟踪环的设计是伪码/载波相位联合测距系统的一个关键环节.分析了伪码跟踪环路的结构,利用查表法、二阶环路分别对NCO和环路滤波器等关键部分进行了设计,并给出了相应的电路结构.系统仿真与FPAG片上测试结果表明,实现了伪码准确、实时跟踪,跟踪到的伪码相位误差小于载波相位的周期长,设计的跟踪环具有一定工程应用价值.     

A residue number system implementation of real orthogonaltransforms

Previous work has focused on performing residue computations that are quantized within a dense ring of integers in the real domain. The aims of this paper are to provide an efficient algorithm for the approximation of real input signals, with arbitrarily small error, as elements of a quadratic number ring and to prove residual number system moduli restrictions for simplified multiplication within the ring. The new approximation scheme can be used for implementation of real-valued transforms and their multidimensional generalizations     

L’arithmétique sur une surface percée

This article gives the principles for diophantine approximation of real numbers by rationals. The measure of the approximation is given, with the general context for Markoff theory. The hyperbolic structure modelling the geometry of quadratic forms associated is presented. The Markoff theory is then interpreted as giving the geodesics bordering the hole of a punctured torus. The geometric interpretation of the class number of quadratic forms on a punctured sphere is also given. More generally, the link is made with Riemann surfaces and the theories of Teichmuller and Thurston for closed surfaces of negative Euler Poincaré characteristic.     

BPSK通信系统的部分最优MIMO检测算法

在BPSK调制下,基于最大似然（Maximum Likelihood,ML）准则的MIMO检测器是一个二进制二次规划问题,其计算复杂度随着天线数的增多呈指数增加,当天线数较多时,其计算量太大,无法满足实时通信的要求。本文提出了一种新的MIMO检测算法。使用新算法,可以在很小的计算开销下,求解出ML检测器的部分全局最优解,然后,将优先检测出的部分最优解从原二进制二次规划问题中剔除得到一个相对小规模问题,最后使用传统的次最优检测算法对该小规模问题进行求解。这样,新算法不仅可以得到比传统的次最优检测器更低的误码率,计算量又远小于ML最优检测器。本文的仿真结果验证了新算法的有效性。      

特征3时椭圆曲线与函数域的DLP等价

论文给出了特征等于3的有限域上,椭圆曲线的有理点群(除去这个点本身)与实二次函数域上的既约主理想之间的一一对应,从而使二者的离散对数问题(DLP)等价。     

A New Public-Key Cryptosystem over a Quadratic Order with Quadratic Decryption Time

We present a new cryptosystem based on ideal arithmetic in quadratic orders. The method of our trapdoor is different from the Diffie—Hellman key distribution scheme or the RSA cryptosystem. The plaintext m is encrypted by mp ^r , where p is a fixed element and r is a random integer, so our proposed cryptosystem is a probabilistic encryption scheme and has the homomorphy property. The most prominent property of our cryptosystem is the cost of the decryption, which is of quadratic bit complexity in the length of the public key. Our implementation shows that it is comparably as fast as the encryption time of the RSA cryptosystem with e=2 ¹⁶ +1 . The security of our cryptosystem is closely related to factoring the discriminant of a quadratic order. When we choose appropriate sizes of the parameters, the currently known fast algorithms, for example, the elliptic curve method, the number field sieve, the Hafner—McCurley algorithm, are not applicable. We also discuss that the chosen ciphertext attack is not applicable to our cryptosystem. Received 29 June 1998 and revised 15 November 1998     

One Dimensional Inverse Dielectric Profiling of Embedded Slabs by a Quadratic Approximation

In this paper the inverse problem of the determination of the dielectric profile of a slab embedded into a homogeneous half space starting from the knowledge of the scattered field for different illumination angles is considered. A comparison between the features of a linear and a quadratic distorted approximation of the scattering problem is carried out, in order to determine the kind of profiles that can be reconstructed. In particular, the investigation of the direct problem reveals that, under the linear approximation, only a limited number of Fourier harmonics of the profile give contribution to the scattered field. The use of the quadratic approximation allows to change the number and order of the harmonic that can be imaged. The dependence of the results on the dielectric permittivity of the host medium is also highlighted. Numerical examples support the theoretical considerations.     

一种基于二次型的无线传感器网络密钥管理方案

针对现有的基于多项式的密钥预分配管理方案受限于节点间密钥共享率和网络连通率等问题,文中提出了一种基于二次型的无线传感器密钥管理方案.该方案突破现有二元t次对称多项式建立共享密钥的思路,引入多元非对称二次型多项式,利用二次型特征值与特征向量之间的关系,分析证明二次型正交对角化的特性,生成密钥信息,节点则通过交换密钥信息实现身份认证,生成与邻居节点之间独立唯一的会话密钥.性能分析表明,与现有的密钥管理方案相比,方案在抗俘获性、连通性、可扩展性、通信开销和存储开销上有较大的改进.     

Quadratic Gabor filters for object detection

We present a new class of quadratic filters that are capable of creating spherical, elliptical, hyperbolic and linear decision surfaces which result in better detection and classification capabilities than the linear decision surfaces obtained from correlation filters. Each filter comprises of a number of separately designed linear basis filters. These filters are linearly combined into several macro filters; the output from these macro filters are passed through a magnitude square operation and are then linearly combined using real weights to achieve the quadratic decision surface. For detection, the creation of macro filters (linear combinations of multiple single filters) allows for a substantial computational saving by reducing the number of correlation operations required. In this work, we consider the use of Gabor basis filters; the Gabor filter parameters are separately optimized. The fusion parameters to combine the Gabor filter outputs are optimized using an extended piecewise quadratic neural network (E-PQNN). We demonstrate methods for selecting the number of macro Gabor filters, the filter parameters and the linear and nonlinear combination coefficients. We present preliminary results obtained for an infrared (IR) vehicle detection problem.     

Performance of DPSK Signals With Quadratic Phase Noise

Nonlinear phase noise induced by the interaction of the fiber Kerr effect and amplifier noises is a quadratic function of the electric field. When the dependence between the additive Gaussian noise and the quadratic phase noise is taken into account, the error probability for differential phase-shift keying signals is derived analytically. Depending on the number of fiber spans, the signal-to-noise ratio penalty is increased by up to 0.23 dB, due to the dependence between the Gaussian noise and the quadratic phase noise.     

Entropy-controlled quadratic markov measure field models for efficient image segmentation.

We present a new Markov random field (MRF) based model for parametric image segmentation. Instead of directly computing a label map, our method computes the probability that the observed data at each pixel is generated by a particular intensity model. Prior information about segmentation smoothness and low entropy of the probability distribution maps is codified in the form of a MRF with quadratic potentials so that the optimal estimator is obtained by solving a quadratic cost function with linear constraints. Although, for segmentation purposes, the mode of the probability distribution at each pixel is naturally used as an optimal estimator, our method permits the use of other estimators, such as the mean or the median, which may be more appropriate for certain applications. Numerical experiments and comparisons with other published schemes are performed, using both synthetic images and real data of brain MRI for which expert hand-made segmentations are available. Finally, we show that the proposed methodology may be easily extended to other problems, such as stereo disparity estimation.     

Quadratic solitons: recent developments

Multicolor optical solitons mediated by quadratic nonlinearities have been observed experimentally during the last few years in a variety of materials and geometries in a number of laboratories around the world. Today, many of the basic properties of the corresponding soliton families are theoretically well established. Nevertheless, experiments continuously reveal new surprises, and the topic is entering new theoretical and experimental territories. In this paper, we briefly outline the key features of the quadratic solitons and overview the latest developments.     

第二类计算机构想

根据集合论中康托定理等,定位几何曲线被定义为第二类数———f数,并建立了相应的第二类数域F0,它们是对实数、实数域的一种本质性扩充。以第二类数为基本运算单元的计算机,是第二类计算机。人类的视觉等,是第二类计算的一些实际例子。     

HFEM公钥密码方案的设计与实现

基于BMQ问题的困难性,以及有限域上的矩阵与向量之间的关系,提出了一种新的公钥密码方案,即隐藏域上遍历矩阵的公钥密码.给出了有关矩阵集合的约束条件以及利用遍历矩阵来构造满足条件之矩阵集合的方法.与已有MPKC方案相比,HFEM具有陷门设计新颖、算法简单、不涉及任何乘幂及复杂运算、加/解密算法效率相当、中心映射难以抽象、密钥/明文/密文空间大等特点.     

一种新的机载SAR回波高阶多项式相位误差提取方法

当载机在SAR回波方位子孔径时间内运动较复杂时,二次相位误差模型不能准确描述载机运动造成的相位误差。针对此情况,该文借鉴PACE算法的思想,提出了一种提取SAR回波中时域高阶多项式相位误差的TPACE算法。TPACE算法将图像对比度函数作为目标函数,以时域高阶多项式相位误差模型系数作为自变量,通过最优化方法提取时域误差系数。文中详细推导了对比度函数关于误差模型系数的梯度表达式,分析了TPACE与以往提取时域高阶多项式相位误差的算法计算量之差别。实际超宽带SAR回波数据处理结果表明,TPACE能有效提取时域高阶多项式误差,是一种计算量相对较小的SAR自聚焦算法。     

一种4t＋1型素数码长伪随机序列的构造

提出利用有限城的二次特征函数构造４ｔ＋１型素数码长的伪随机序列的方法。并与ｍ序列、Ｍ序列进行比较。     

An adaptive method for combined covariance estimation andclassification

In this paper, a family of adaptive covariance estimators is proposed to mitigate the problem of limited training samples for application to hyperspectral data analysis in quadratic maximum likelihood classification. These estimators are the combination of adaptive classification procedures and regularized covariance estimators. In these proposed estimators, the semi-labeled samples (whose labels are determined by a decision rule) are incorporated in the process of determining the optimal regularized parameters and estimating those supportive covariance matrices that formulate final regularized covariance estimators. In all experiments with simulated and real remote sensing data, these proposed combined covariance estimators achieved significant improvement on statistics estimation and classification accuracy over conventional regularized covariance estimators and an adaptive maximum likelihood classifier (MLC). The degree of improvement increases with dimensions, especially for ill-posed or very ill-posed problems where the total number of training samples is smaller than the number of dimensions     

Rank-2-Optimal Adaptive Design of Binary Spreading Codes

Over the real/complex field, the spreading code that maximizes the signal-to-interference-plus-noise ratio (SINR) at the output of the maximum-SINR linear filter is the minimum-eigenvalue eigenvector of the interference autocovariance matrix. In the context of binary spreading codes, the maximization problem is NP-hard with complexity exponential in the code length. A new method for the optimization of binary spreading codes under a rank-2 approximation of the inverse interference autocovariance matrix is presented where the rank-2-optimal binary code is obtained in lower than quadratic complexity. Significant SINR performance improvement is demonstrated over the common binary hard-limited eigenvector design which is shown to be equivalent to the rank-1-optimal solution.