本文選題：光正交簽名碼 + 填充設(shè)計(jì)��； 參考：《北京交通大學(xué)》2015年博士論文

【摘要】：1994年,Kitayama基于光纖通信技術(shù)在醫(yī)學(xué)圖像、數(shù)字視頻廣播以及超計(jì)算機(jī)可視化圖像傳輸方面的應(yīng)用,提出了一種新型的、采用空間擴(kuò)頻技術(shù)實(shí)現(xiàn)的光碼分多址并行圖像傳輸系統(tǒng).與此同時(shí),光正交簽名碼作為碼分多址并行圖像傳輸系統(tǒng)的首選光地址碼,受到了信息論領(lǐng)域、組合設(shè)計(jì)領(lǐng)域等眾多學(xué)者的關(guān)注. 設(shè)k,m,n,λa和λc為正整數(shù).參數(shù)為(m,n,k,λa,λc)的光正交簽名碼l是一族自相關(guān)系數(shù)為λa,互相關(guān)系數(shù)為λc,且Hamming重量為k的m×n(0,1)-矩陣(碼字),簡(jiǎn)記為(m,n,k,λa,λc)-OSPC一個(gè)光正交簽名碼的碼字容量即為其所包含碼字的個(gè)數(shù),它決定了碼分多址并行圖像傳輸系統(tǒng)能夠同時(shí)承載的最大用戶量.令Θ(m,n,k,λa,λc)表示所有(m,n,k,λa,λc)-OOSPC中碼字容量的最大值,則稱碼字容量為Θ(m,n,k,λa,λc)的(m,n,k,λa,λc)-OOSPC是最優(yōu)的(或最大的).當(dāng)λa=λc=λ時(shí),記號(hào)(m,n,k,λa,λc)-OOSPC與Θ(m,n,k,λa,λc)分別簡(jiǎn)寫為(m,n,k,λa,λc)-OOSPC與Θ(m,n,k,λ) 本文主要圍繞如下的兩個(gè)問題展開深入討論. (1)如何確定Θ(m,n,k,λa,λc)的精確值? (2)如何構(gòu)作碼字容量為Θ(m,n,k,λa,λc)的最優(yōu)(m,n,k,λa,λc)-OOSPC 文章結(jié)構(gòu)組織如下. 第1章簡(jiǎn)要介紹光正交簽名碼的研究背景、意義以及現(xiàn)狀. 第2章探討最優(yōu)(m,n,k,λa,λc)-OOSPC碼字容量的計(jì)算問題.利用有限群理論中群作用的思想給出λα=k或k-1情形下,Θ(m,n,k,λa,k-1)值的計(jì)算公式. 第3章從組合設(shè)計(jì)理論的角度出發(fā),剖析光正交簽名碼的組合結(jié)構(gòu),指出光正交簽名碼與一類特殊填充設(shè)計(jì)之間的等價(jià)關(guān)系.進(jìn)一步地,借助組合設(shè)計(jì)理論中的兩類輔助設(shè)計(jì)：差陣與可分組設(shè)計(jì),給出(m,n,k,λa,λc)-OOSPC的一系列遞歸構(gòu)作.除此之外,還將以(3,n,4,1)-OOSPC為例,介紹兩種直接構(gòu)作光正交簽名碼的方法,同時(shí)給出(3,n,4,1)-OOSPC的一些無窮類. 第4與第5章將利用第3章給出的諸多構(gòu)作方法去解決最優(yōu)(m,n,4,1)-OOSPC和最優(yōu)(m,n,3,1)-OOSPC的構(gòu)作問題.其中,第4章主要是拓展(m,n,4,1)-OOSPC的已有結(jié)果.最終圍繞三類參數(shù)：(1)gcd(m,18)=3且n三0(mod12),(2)mn三8,16(mod24)且gcd(m,n,2):2,及(3)mn三0(mod24)且gcd(m,n,6)=2,獲得最優(yōu)(m,n,4,1)-OOSPC的若干無窮類.第5章則是在第3章所給構(gòu)作方法的基礎(chǔ)上,針對(duì)某些特殊參數(shù)下的(m,n,3,1)-OOSPC,創(chuàng)新出新的構(gòu)作方法,從而使得最優(yōu)(m,n,3,1)-OOSPC的構(gòu)作問題得以徹底解決. 基于差陣在遞歸構(gòu)作光正交簽名碼時(shí)的應(yīng)用,第6章集中探討了有限交換群G上(G,4,λ)差陣(即(G,4,λ)-DM)的存在性問題.最終針對(duì)λ=1且G為非循環(huán)交換群,以及λ1為奇數(shù)且G為交換群兩種情形,證明了(G,4,λ)-DM存在的充要條件是G沒有循環(huán)的Sylow2-子群.除此之外,還在第6章的末尾指出,對(duì)任意偶數(shù)λ≥2和任意有限交換群G,(G,4,λ)-DM總是存在的.
[Abstract]:Based on the application of optical fiber communication technology in medical image, digital video broadcasting and visual image transmission by supercomputer in 1994, Kitayama proposed a new optical code division multiple access (OCDMA) parallel image transmission system using spatial spread spectrum technology. At the same time, optical orthogonal signature codes, as the first choice of optical address codes for code division multiple access (CDMA) parallel image transmission systems, have attracted much attention from many scholars in the field of information theory, combinatorial design and so on. Let k n, 位 a and 位 c be positive integers. The optical orthogonal signature code l with the parameters of Hamming, 位 _ a, 位 _ c is a family of autocorrelation coefficient 位 _ a, and the correlation number is 位 _ c, and the Hamming weight k is m 脳 n ~ (0) ~ (1) ~ (-1) matrix. The codeword capacity of an optical orthogonal signature code is the number of the code words contained in the optical orthogonal signature code (位 _ (a), 位 _ (a) 位 _ (c), and the number of the code words contained in the code is the same as the number of the code words contained in the optical orthogonal signature code (位 _ a, 位 _ (a), 位 _ c)-OSPC). It determines the maximum number of users that the code division multiple access (CDMA) parallel image transmission system can carry at the same time. In this paper, we make mmmnnnnk, 位 _ a, 位 _ c denote the maximum capacity of all codewords in c)-OOSPC, then we say that the code-word capacity is mmnnk, 位 _ (a, 位 _ c) is the best (or the largest) of which the codeword capacity is mnnnnk, 位 _ (a, 位 _ c), 位 _ (a), 位 _ (a, 位 _ c) is the best (or the largest). When 位 _ a = 位 _ c = 位 _ c, the notation c)-OOSPC, 位 _ a, 位 _ c)-OOSPC and ~ (?) are abbreviated as "mechnik, 位 _ a, 位 _ c), respectively). 位 _ a, 位 _ (c)-OOSPC) and ~ () ~ = 位, 位 _ _ _ This paper focuses on the following two issues are discussed in depth. (1) how to determine the exact value of themnnhk, 位 _ a, 位 _ c)? (2) how to construct the optimal c)-OOSPC of a codeword with a capacity of -, 位 _ (a, 位 _ c) (= The structure of the article is as follows. Chapter 1 briefly introduces the research background, significance and current situation of optical orthogonal signature codes. In chapter 2, we discuss the calculation of the optimal c)-OOSPC codeword capacity. By using the idea of group action in the finite group theory, the formulas for calculating the value of 位 偽 ~ (n) k or k ~ (-1) in the case of 位 _ 偽 _ k or k ~ (-1) are given. In chapter 3, the combinatorial structure of optical orthogonal signature codes is analyzed from the point of view of combinatorial design theory, and the equivalent relationship between optical orthogonal signature codes and a class of special fill designs is pointed out. Furthermore, with the aid of two kinds of auxiliary design in combinatorial design theory: difference matrix and grouping design, a series of recursive constructions of c)-OOSPC are given. In addition, two methods of directly constructing optical orthogonal signature codes are introduced, and some infinite classes of OOSPC are given. In the fourth and fifth chapters, we will solve the construction problems of the optimal MNU 4OOSPC and the OOSPC by using the construction methods given in Chapter 3. The results show that the structure of the OOSPC is better than that of the OOSPC, and that of the OOSPC is better than that of the OOSPC. Among them, chapter 4 is mainly to expand the existing results of OOSPC. Finally, around three parameters: 1 / 1 / g / d / m ~ (18) / 3 and n ~ 30 / 0 / d ~ (12) / ~ (2) mn ~ (3 / 8) / ~ (16) ~ (24) and 3 / 3 / mn ~ (30) mod24) and / or gcdlum / mn ~ (6) / 2), some infinite classes of OOSPC are obtained. In chapter 5, on the basis of the construction method given in chapter 3, a new construction method is innovated for some special parameters. Based on the application of differential matrix in the recursive construction of optical orthogonal signature codes, in chapter 6, we focus on the existence of the differential matrices (i.e., G ~ (4), 位 ~ (-DM) over a finite commutative group G. In this paper, we prove that G is a noncyclic commutative group and 位 1 is odd and G is a commutative group. The necessary and sufficient condition is that G does not have a cyclic Sylow2-subgroup. In addition, at the end of Chapter 6, it is pointed out that for any even number 位 鈮，

本文編號(hào)：1918285