给定线性复杂度谱的序列的条数

对给定长为n的单调递增非负整数序列(L1,L2,…,Ln),给出了有限域GF(q)上长度为n的线性复杂度谱为(L1,L2,…,Ln)的序列的计数。进一步对长为n的给定线性复杂度及其最大跳跃幅度的序列进行了计数。     

New classes of almost bent and almost perfect nonlinear polynomials

New infinite classes of almost bent and almost perfect nonlinear polynomials are constructed. It is shown that they are affine inequivalent to any sum of a power function and an affine function.     

Dimension/length profiles and trellis complexity of linear blockcodes

This semi-tutorial paper discusses the connections between the dimension/length profile (DLP) of a linear code, which is essentially the same as its “generalized Hamming weight hierarchy”, and the complexity of its minimal trellis diagram. These connections are close and deep. DLP duality is closely related to trellis duality. The DLP of a code gives tight bounds on its state and branch complexity profiles under any coordinate ordering; these bounds can often be met. A maximum distance separable (MDS) code is characterized by a certain extremal DLP, from which the main properties of MDS codes are easily derived. The simplicity and generality of these interrelationships are emphasized     

Solving sparse linear equations over finite fields

A "coordinate recurrence" method for solving sparse systems of linear equations over finite fields is described. The algorithms discussed all requireO(n_{1}(omega + n_{1})log^{k}n_{1})field operations, wheren_{1}is the maximum dimension of the coefficient matrix,omegais approximately the number of field operations required to apply the matrix to a test vector, and the value ofkdepends on the algorithm. A probabilistic algorithm is shown to exist for finding the determinant of a square matrix. Also, probabilistic algorithms are shown to exist for finding the minimum polynomial and rank with some arbitrarily small possibility of error.     

Channels with almost finite memory

A stationary channel can have two kinds of memory--input memory and output memory. Recently, Gray and Ornstein introduced a condition on the decay of input memory calledbar{d}-continuity and established coding theorems for d-continuous channels. In this paper a condition for the decay of output memory is introduced which is called conditional almost block independence (CABI). It is believed that these two properties describe the character of many channels of interest. The principal result states that thebar{d}-continuous CABI channels are precisely those which can be approximated in a very strong sense by a simple kind of finite memory channel, called a primitive channel, in which the source of randomness is memoryless and completely separated from the memory.     

Multiplicative complexity of bilinear algorithms for cyclic convolution over finite fields

The multiplicative complexity of bilinear algorithms for cyclic convolution over finite fields is investigated. It is shown that mutually prime factor algorithms are inferior to directly designed algorithms for all lengths except those whose factors have relatively prime exponents. A previously described approach is proposed for directly designing algorithms which are highly structured and computationally efficient. Several complexity results are provided for factor lengths of specific form, and the manner in which cyclic convolution algorithms lead to linear algebraic error-correcting codes is discussed.Research supported by Natural Sciences and Engineering Research Council Canada Grant A0912.     

Synthesis of monomode fibre profiles by solving an almost linear system of algebraic equations

The letter describes a new method for the synthesis of monomode fibre profiles. By solving a system of almost linear algebraic equations this approach allows an index profile to be calculated from a specified functional relation of the dispersion coefficient. As an example the index profile of a broadband fibre was determined.     

近完美序列与m序列的分析和比较

理想周期伪随机序列的异相自相关全为零,被称为完美序列.然而已证明在周期为4< n<12100范围内不存在完美序列,因此,异相自相关系数中除中间的一点外全为零的近完美序列在一定条件下可替代完美序列.与常用的m序列相比,近完美序列可以实现无旁瓣测距,从而有效解决近区大功率回波旁瓣淹没远区小功率回波主瓣的问题.同样长度的m序列和近完美序列被用于武汉电离层斜向返回探测系统进行实测比较,结果显示,在同样的发射功率和探测波形参数下,近完美序列探测获得的后向散射回波具有更高的信噪比.     

pmqn周期q元序列线性复杂度与k错复杂度的关系

研究了q元周期序列线性复杂度和k错复杂度之间的关系,给出了k错复杂度严格小于线性复杂度的一个充要条件.当周期为N=pqn时,给出了使得LC(S+E)＜LC(S)成立的错误多项式EN(x)的确切表达式,以及使得LCk(S)＜LC(S)成立的最小的k值,即minerror(S)的值,结果表明minerror(S)与线性复杂度的重量密切相关;当周期为N=pmqn时,给出了使得LC(S+E)＜LC(S)成立的用错误多项式EN(x)表达的一个充分条件.这里P为奇素数,q是素数且是一个模p2的本原根.     

Periodic sequences with large k-error linear complexity

We establish the existence of periodic sequences over a finite field which simultaneously achieve the maximum value (for the given period length) of the linear complexity and of the k-error linear complexity for small values of k. This disproves a conjecture of Ding, Xiao, and Shan (1991). The result is of relevance for the theory of stream ciphers.     

Estimation of co-channel signals with linear complexity

To increase wireless system capacity using co-channel signals and multiple receiver antennas, we develop the partitioned Viterbi algorithm (PVA). The PVA estimation complexity increases linearly with each additional co-channel signal rather than exponentially as it does with joint maximum-likelihood sequence estimation (MLSE). The estimation problem involves multiple signals simultaneously transmitted and observed through slow-fading, frequency-selective channels. Although transmission is assumed to be in bursts according to a time-division multiple-access scheme, more than one signal can occupy the same time and frequency slot (these signals are referred to as “co-channel” signals). Separation and estimation of the symbol bursts is accomplished by exploiting channel differences, PVA estimation consists of a set of Viterbi detectors, one per signal, that operate in parallel with cross-coupling to allow approximate interference cancellation by means of tentative decisions. The forward filter of a decision feedback equalizer (DFE) is used to “prefilter” received signals prior to PVA estimation. Prefiltering delays the energy of interfering signals so that tentative decisions become reliable enough to use. Simulation results show PVA performance remains near-optimal with respect to the performance of joint MLSE     

Products of linear recurring sequences with maximum complexity

Conditions are derived which guarantee that products of linear recurring sequences attain maximum linear complexity. It is shown that the product of any number of maximum-length GF(q)sequences has maximum linear complexity, provided only the degrees of the corresponding minimal polynomials are distinct and greater than two. It is also shown that if the roots of any number of (not necessarily irreducible) minimal polynomials are simple and lie in extension fields of pairwise relatively prime degrees, then the product of the corresponding GF(q)sequences attains maximum linear complexity, provided only that no two roots of any minimal polynomial are linearly dependent over the groundfield GF(q)(which is automatically satisfied whenq = 2). The results obtained for products are extended to arbitrary linear combinations of product sequences.     

2mpn周期二元序列的线性复杂度和k错线性复杂度

序列线性复杂度的稳定性是衡量其随机性好坏的一个重要指标.针对2mpn周期二元序列,利用多项式分解等工具,确定了使得序列的k错线性复杂度严格小于其线性复杂度的最小k值的上下界,其中n是正整数,m是非负整数,P是奇素数,2是模p2的原根.     

Surface fields and near fields of a linear antenna

In a variational impedance formulation, antenna trial functions are modified to satisfy the edge conditions of diffraction theory. For a half-wave antenna, this provides a charge distribution with experimentally verified linear portions. The linearity of the charge distribution appears to be correlated with near-field fluctuations of the antenna.     

二元周期序列的线性复杂率与k-错复杂度的关系

k-错复杂度是指改变序列一个周期段中k个或少于k个符号后所得序列的最小线性复杂度。该文讨论了周期为2~pq(q为奇素数,2是模q~2的本原根)的二元序列线性复杂度与k的关系,这里k是满足LC_k(S~N)相似文献   

Analysis of fields and coupling associated with optical fibers withpower-law profiles

The fundamental mode fields of optical fibers are of importance for various applications. The field and relevant properties are directly related to the index profile of the fiber itself. In practice, index profiles for many fibers can be represented by power-law functions. Within the framework of a field approximation method the authors systematically study fundamental mode fields of optical fibers with clad power-law profiles, as well as coupling occurring between two such fibers     

Density/length profiles and trellis complexity of lattices

The density/length profile (DCP) of a lattice Λ is analogous to the dimension/length profile of a linear code. The DLP is a geometrical invariant of Λ that includes the coding gain of Λ. Duality results analogous to those of linear block codes are derived for lattices. Bounds on the DLP may be derived from bounds on Hermite's constants; these hold with equality for many dense lattices. In turn, the DLP lowerbounds the state complexity profile of a minimal trellis diagram for Λ in any coordinate system. It is shown that this bound can be met for the E₈ lattice by a laminated lattice construction with a novel trellis diagram. Bounds and constructions for other important low-dimensional lattices are given. Two laminated lattice constructions of the Leech lattice yield trellis diagrams with maximum state space sizes 1024 and 972     

周期为4v(几乎)平衡理想二进制序列构造研究

具有理想自相关特性的序列在无线通信、雷达以及密码学中具有重要的作用.因此为了扩展更多可应用于通信系统的理想序列,该文基于2阶分圆类和中国剩余定理,提出3类新的周期为T=4v(v是奇素数)平衡或几乎平衡理想二进制序列构造方法.构造所得序列的周期自相关函数满足:当v≡3(mod4)时,序列的周期自相关函数旁瓣值取值集合为{...     

Capacity maximizing in massive MIMO with linear precoding for SSF and LSF channel with perfect CSI

The capacity of a massive MIMO cellular network depends on user and antenna selection algorithms, and also on the acquisition of perfect Channel State Information (CSI). Low computational cost algorithms for user and antenna selection significantly may enhance the system capacity, as it would consume a smaller bandwidth out of the total bandwidth for downlink transmission. The objective of this paper is to maximize the system sum-rate capacity with efficient user and antenna selection algorithms and linear precoding. We consider in this paper, a slowly fading Rayleigh channel with perfect acquisition of CSI to explore the system sum-rate capacity of a massive MIMO network. For user selection, we apply three algorithms, namely Semi-orthogonal user selection (SUS), Descending Order of SNR-based User Scheduling (DOSUS), and Random User Selection (RUS) algorithm. In all the user selection algorithms, the selection of Base Station (BS) antenna is based on the maximum Signal-to-Noise Ratio (SNR) to the selected users. Hence users are characterized by having both Small Scale Fading (SSF) due to slowly fading Rayleigh channel and Large-Scale Fading (LSF) due to distances from the base station. Further, we use linear precoding techniques, such as Zero Forcing (ZF), Minimum Mean Square Error (MMSE), and Maximum Ratio Transmission (MRT) to reduce interferences, thereby improving average system sum-rate capacity. Results using SUS, DOSUS, and RUS user selection algorithms with ZF, MMSE, and MRT precoding techniques are compared. We also analyzed and compared the computational complexity of all the three user selection algorithms. The computational complexities of the three algorithms that we achieved in this paper are O(1) for RUS and DOSUS, and O(M²N) for SUS which are less than the other conventional user selection methods.     

一种低差错平底线性复杂度的QC-LDPC码构造方法

本文给出了一种低差错平底QC-LDPC码构造方法.首先,提出了扩展近似下三角阵eALT( extern Approximate Lower Triangular)的全局矩阵构造法,通过对改进后的全局矩阵M进行矩阵置换,生成LDPC码的校验矩阵H以达 到减少小停止集( Stopping Set)数量,降低差错平台(Er...