Two constructions of permutation arrays

In this correspondence, two new constructions of permutation arrays are given. A number of examples to illustrate the constructions are also provided.     

Constructions and properties of Costas arrays

A Costas array is an n × n array of dots and blanks with exactly one dot in each row and column, and with distinct vector differences between all pairs of dots. As a frequency-hop pattern for radar or sonar, a Costas array has an optimum ambiguity function, since any translation of the array parallel to the coordinate axes produces at most one out-of-phase coincidence. We conjecture that n × n Costas arrays exist for every positive integer n. Using various constructions due to L. Welch, A. Lempel, and the authors, Costas arrays are shown to exist when n = p - 1, n = q - 2, n = q - 3, and sometimes when n = q - 4 and n = q - 5, where p is a prime number, and q is any power of a prime number. All known Costas array constructions are listed for 271 values of n up to 360. The first eight gaps in this table occur at n = 32, 33, 43, 48, 49, 53, 54, 63. (The examples for n = 19 and n = 31 were obtained by augmenting Welch's construction.) Let C(n) denote the total number of n × n Costas arrays. Costas calculated C(n) for n ≤ 12. Recently, John Robbins found C(13) = 12828. We exhibit all the arrays for n ≤ 8. From Welch's construction, C(n) ≥ 2n for infinitely many n. Some Costas arrays can be sheared into "honeycomb arrays." All known honeycomb arrays are exhibited, corresponding to n = 1, 3, 7, 9, 15, 21, 27, 45. Ten unsolved problems are listed.     

Investigation of a setup procedure for triangular permutation arrays

A setup procedure for setting all the cells of a triangular permutation network is described. This procedure is based on an earlier published inductive proof of the ability of the triangular array to set up any input/output permutation. The procedure requires N?1 step to set up a size-N triangular array, and can be easily programmed or implemented using straightforward hardware techniques. Various simple extensions of this procedure were also investigated to reduce the average number of cells to be switched from one mode (bend or cross) to another.     

Golomb Costas序列的结构及其在OFDM系统中的应用

研究了用循环移位法获得的Golomb Costas序列族的特性,建立了含有一个间隙行和一个间隙列的Golomb Costas序列的结构理论,深入研究了含有一个间隙行和一个间隙列的Golomb Costas序列的代数结构、构造方法和自（互）相关特性,并证明了相关的定理。探索了用含有一个间隙行和一个间隙列的Golomb Costas序列设计OFDM 系统中跳频图样的方法,举例说明了如何设计跳频码和怎样将跳频码分配给 OFDM 系统中的用户。用含有一个间隙行和一个间隙列的Golomb Costas序列设计跳频码能获得理想的自相关特性,并且当无线通信系统中多普勒频移受限时能获得极佳的互相关性能。     

Vector permutation modulation

This article introduces a new class of codes for transmission over a Gaussian channel. The new scheme, named vector permutation modulation (VPM), is an extension of Slepian's (scalar) permutation modulation (SPM) to the case where codeword components are L-dimensional vectors. A method is presented for maximum-likelihood detection in additive white Gaussian noise and fading channels. Since SPM is a special case of VPM, this method can also be used for SPM detection in fading channels. We solve the problem of finding the reference codeword, which maximizes code rate for a given average energy. It is shown that VPM performs significantly better than its scalar counterpart.     

Optimized permutation modulation

Permutation modulation is a class of group codes for the Gaussian channel. A group code is a set of vectors obtained by a group of orthogonal matrices operating on an initial vector. An important problem is to find the initial vector yielding the largest minimum Euclidean distance between two vectors. This problem is solved for permutation modulation. The performance of such optimized permutation modulation is analyzed. Compared to binary antipodal signals and PSK (phase-shift keying), it typically requires 2.5-4 dB less energy for the same minimum distance     

Constructions of algebraic-geometry codes

Based on curves over finite fields with many rational points, we present two constructions of linear codes from local expansions of functions at a fixed rational point. It turns out that codes from our constructions have the same bound on their parameters as Goppa's (1981) geometry codes. Furthermore, we prove that our second construction is equivalent to Goppa's construction. Finally, an additional construction of linear codes from maximal curves shows that these codes have better parameters than Goppa's geometry codes from maximal curves for a certain interval of parameters     

Z_n上的全向置换

本文给出Ｚｎ上全向置换这一概念,讨论全向置换的存在性、函数特性、构造和计数等问题。得到了Ｚｎ上全向置换的存在性定理、不动点特征以及利用正交拉丁方构造全向置换的一种方法,并对全向置换的计数问题进行了研究。     

On optimal permutation codes

Permutation codes are vector quantizers whose codewords are related by permutations and, in one variant, sign changes. Asymptotically, as the vector dimension grows, optimal Variant I permutation code design is identical to optimal entropy-constrained scalar quantizer (ECSQ) design. However, contradicting intuition and previously published assertions, there are finite block length permutation codes that perform better than the best ones with asymptotically large length; thus, there are Variant I permutation codes whose performances cannot be matched by any ECSQ. Along similar lines, a new asymptotic relation between Variant I and Variant II permutation codes is established but again demonstrated to not necessarily predict the performances of short codes. Simple expressions for permutation code performance are found for memoryless uniform and Laplacian sources. The uniform source yields the aforementioned counterexamples     

Constructions of intersecting codes

New constructions of binary linear intersecting codes are presented. Some codes with high distances are shown to be intersecting     

Constructions of particular random processes

This paper reviews how to construct sets of random numbers with particular amplitude distributions and correlations among values. These constructions support both high-fidelity Monte Carlo simulation and analytic design studies. A variety of constructions is presented to free engineering models from “white or normal” limitations embodied in many current simulations. The methods support constructions of conventional stationary and normally distributed processes, nonstationary, nonnormal signal and interference waveforms, nonhomogeneous random scenes, nonhomogeneous volumetric clutter realizations, and snapshots of randomly evolving, nonhomogeneous scenes. Each case will have specified amplitude statistics, e.g., normal, log-normal, uniform, Weibull, or discrete amplitude statistics; and selected correlation, e.g., white, pink, or patchy statistics, clouds. or speckles. Sets of random numbers with correlation, nonstationarities, various tails for the amplitude distributions, and multimodal distributions can be constructed. The paper emphasizes aspects of probability theory necessary to engineering modeling     

“多核技术”课程建设研究

本文介绍了我校在"多核技术"课程建设中采取的具体举措,包括完善教学内容,动画演示,录屏视频辅助,考试和实践相结合等方法。笔者通过改进教学方法来提高教学效果,提高学生学习积极性和主动性。教学实践表明:"多核技术"课程的教学方法在教学实践中取得了良好的教学效果。     

Algorithms for permutation channel routing

In this paper the channel routing problem is generalized to allow the interchange of some of the pins in the channel. The generalized problem is called the Permutation Channel Routing Problem (PCRP). This model arises naturally when there are logically equivalent (and therefore interchangeable) pins. Various other applications of the model are also presented. We show that the PCRP is NP-complete for two different cost measures. An optimal algorithm is presented for a special case called the Single Permutable Block Model. For the general PCRP, we study two methods of solution: iterative improvement and simulated annealing. Our results show that allowing some of the pins to be interchanged can lead to a substantial reduction in the number of tracks needed for routing. For example, by randomly generating a few small groups of interchangeable pins, a savings of 42% was obtained for Deutsch's Difficult problem. For all the test problems, our algorithms produce results that are very close to the best possible ones. We also show that our algorithms outperform a previous method by Kobayashi and Drozd.     

Optimum quantizers and permutation codes

Amplitude quantization and permutation encoding are two of the many approaches to efficient digitization of analog data. It is shown in this paper that these seemingly different approaches actually are equivalent in the sense that their optimum rate versus distortion performances are identical. Although this equivalence becomes exact only when the quantizer output is perfectly entropy coded and the permutation code block length is infinite, it nonetheless has practical consequences both for quantization and for permutation encoding. In particular, this equivalence permits us to deduce that permutation codes provide a readily implementable block-coding alternative to buffer-instrumented variable-length codes. Moreover, the abundance of methods in the literature for optimizing quantizers with respect to various criteria can be translated directly into algorithms for generating source permutation codes that are optimum for the same purposes. The optimum performance attainable with quantizers (hence, permutation codes) of a fixed entropy rate is explored too. The investigation reveals that quantizers with uniformly spaced thresholds are quasi-optimum with considerable generality, and are truly optimum in the mean-squared sense for data having either an exponential or a Laplacian distribution. An attempt is made to provide some analytical insight into why simple uniform quantization is so good so generally.     

Waveform transmission with permutation modulation

The permutation-modulation scheme proposed by Slepian is applied to waveform transmission. The system performances are described in terms of output signal-to-noise ratio, and a comparison is made with a p.c.m./f.s.k. system.     

随机置换的有关概率问题

基于随机选取0,1,…n?1的置换建立了概率模型,求出了这种随机选取意义下置换后Zn中点与原相邻点之间距离(简称距离)的分布律以及距离为a(1≤a≤n?1)的点个数的数学期望与方差,当距离a和置换阶数n互素时,得到了距离为a的点个数的分布律。依据这些结论分析了随机置换的相关密码安全性问题,对在密码设计中采用全距置换的意义提供了新的解释。     

Constructions of error-correcting DC-free block codes

Two DC-free codes are presented with distance 2d, b ⩾1 length 2n+2r(d-1) for d⩽3 and length 2n+2r(d-1)(2d -1) for d>3, where r is the least integer ⩾log₂ (2n+1). For the first code l=4, c=2, and the asymptotic rate of this code is 0.7925. For the second code l=6, c=3, and the asymptotic rate of this code is 0.8858. Asymptotically, these rates achieve the channel capacity. For small values of n these codes do not achieve the best rate. As an example of codes of short length with good rate, the author presents a (30, 10, 6, 4) DC-free block code with 2²¹ codewords. A construction is presented for which from a given code C ₁ of length n, even weight, and distance 4, the author obtains a (4n, l, c, 4) DC-free block code C₂, where l is 4, 5 or 6, and c is not greater than n+1 (but usually significantly smaller). The codes obtained by this method have good rates for small lengths. The encoding and decoding procedures for all the codes are discussed     

Some Universal Constructions of Autonomic Systems

Self-* is widely considered as a foundation for autonomic computing. The notion of autonomic systems (ASs) and self-* serves as a basis on which to build our intuition about category of ASs in general. In this paper we will specify ASs and self-* and then move on to consider some universal constructions such as products, coproducts, finite limits and colimits of ASs. All of this material is taken as an investigation of our category, the category of ASs, which we call AS.     

周期准互补序列集构造法

该文基于2元序列支撑集和低相关序列集,提出一种新的周期准互补序列集构造框架。在此框架基础上,分别利用最优4元序列族A、族D和Luke序列集提出了3类渐近最优和渐近几乎最优周期准互补序列集,序列集参数由2元序列和低相关序列集共同决定。与传统的完备互补序列集相比,所构造的准互补序列集具有更多的序列数目,应用到多载波扩频通信系统中可以支持更多的用户。     

“机器人控制”课程建设研究

本文介绍了我校“机器人控制”课程建设的若干具体举措,主要包括：完善教学内容,注重板书、课件、动画、视频、研讨和实践的有机结合,革新教学方法,深化评价体系,综合评定学生的学习效果.实践表明,“机器人控制”课程的诸多建设成果是合理的,在教学中取得了良好的教学效果.