發(fā)布時(shí)間：2018-05-26 04:41

  本文選題：網(wǎng)絡(luò)編碼 + 網(wǎng)絡(luò)糾錯(cuò)碼　； 參考：《西安電子科技大學(xué)》2014年博士論文

【摘要】：網(wǎng)絡(luò)編碼理論的創(chuàng)立是21世紀(jì)初通信和信息論領(lǐng)域的重大突破，其核心思想是允許網(wǎng)絡(luò)中間節(jié)點(diǎn)對(duì)輸入信息做線性或非線性的編碼處理后再轉(zhuǎn)發(fā)。網(wǎng)絡(luò)編碼是一種融合了路由和編碼的信息傳輸機(jī)制，已經(jīng)被證明在提高吞吐量、數(shù)據(jù)安全、魯棒性、普適性、負(fù)載均衡及低計(jì)算復(fù)雜性等方面具有很大優(yōu)勢(shì)。目前，網(wǎng)絡(luò)編碼已成為網(wǎng)絡(luò)和通信領(lǐng)域的研究熱點(diǎn)。在此帶動(dòng)之下，許多數(shù)學(xué)方法被應(yīng)用到網(wǎng)絡(luò)編碼理論的研究當(dāng)中，主要包括代數(shù)、圖論、擬陣論、組合與優(yōu)化等等。 網(wǎng)絡(luò)編碼的一個(gè)基本問(wèn)題是理解容量區(qū)域并研究達(dá)到容量界的編碼類型。利用擬陣這一數(shù)學(xué)工具構(gòu)造有效的網(wǎng)絡(luò)編碼方案及研究多源多宿網(wǎng)絡(luò)編碼的容量區(qū)域成為當(dāng)前網(wǎng)絡(luò)編碼領(lǐng)域重要的研究課題之一。本文著重研究了擬陣在確定編碼容量區(qū)域的邊界、構(gòu)造線性網(wǎng)絡(luò)糾錯(cuò)編碼等方面的應(yīng)用，取得的主要成果包括以下幾個(gè)方面： 1.根據(jù)Dougherty等人提出的構(gòu)造可擬陣化網(wǎng)絡(luò)的方法和步驟得到了與向量擬陣R8相關(guān)的網(wǎng)絡(luò)，，并利用Ingleton不等式和張-揚(yáng)非香農(nóng)型信息不等式得到了該網(wǎng)絡(luò)編碼容量的一個(gè)上界。 2.利用擴(kuò)展網(wǎng)絡(luò)與擴(kuò)展全局編碼核等概念，刻畫(huà)了線性網(wǎng)絡(luò)糾錯(cuò)碼與可表示擬陣的關(guān)系。根據(jù)線性網(wǎng)絡(luò)糾錯(cuò)碼的本質(zhì)特征，改進(jìn)了Prasad等提出的可擬陣化糾錯(cuò)網(wǎng)絡(luò)的定義，將其推廣到線性網(wǎng)絡(luò)糾錯(cuò)碼在不同的信宿節(jié)點(diǎn)（集）具有不同的糾錯(cuò)能力的情形。隨后，并研究了單信源可擬陣化網(wǎng)絡(luò)與線性多播/線性廣播/線性擴(kuò)散網(wǎng)絡(luò)糾錯(cuò)MDS碼的關(guān)系。 3.提出了一種基于二階射影線性群PGL(2, p)的子群H上的雙層群網(wǎng)絡(luò)編碼方法，證明了群直積H n中的雙層群網(wǎng)絡(luò)碼可利用加法群Z p與Zp1上的n-長(zhǎng)線性碼構(gòu)造而成。最后，用一個(gè)可擬陣化網(wǎng)絡(luò)的實(shí)例說(shuō)明了所提出的編碼方案在可達(dá)容量區(qū)域方面的優(yōu)勢(shì)。
[Abstract]:The establishment of network coding theory is a great breakthrough in the field of communication and information theory at the beginning of the 21st century. Its core idea is to allow network intermediate nodes to do linear or nonlinear coding processing of input information and then forward it. Network coding is a kind of information transmission mechanism which combines routing and coding. It has been proved to have great advantages in improving throughput, data security, robustness, universality, load balancing and low computational complexity. At present, network coding has become a research hotspot in the field of network and communication. As a result, many mathematical methods have been applied to the research of network coding theory, including algebra, graph theory, matroid theory, combination and optimization, and so on. One of the basic problems of network coding is to understand the capacity region and study the coding types that reach the capacity bound. Using matroid as a mathematical tool to construct an effective network coding scheme and to study the capacity region of multi-source and multi-home network coding has become one of the most important research topics in the field of network coding. This paper focuses on the application of matroids in determining the boundary of coding capacity region and constructing linear network error correction coding. The main results obtained include the following aspects: 1. According to the method and steps of constructing matroid network proposed by Dougherty et al, the network related to vector matroid R8 is obtained, and an upper bound of the coding capacity of the network is obtained by using Ingleton inequality and Zhang Yangfei Shannon type information inequality. 2. By using the concepts of extended network and extended global coding kernel, the relationship between linear network error correction codes and representable matroids is described. According to the essential characteristics of error-correcting codes in linear networks, the definition of matroid error-correcting networks proposed by Prasad et al is improved, which is extended to the cases where linear network error-correcting codes have different error-correcting capabilities at different lock-in nodes (sets). Then, the relationship between single source matroid network and linear multicast / linear broadcast / linear diffusion network error correction MDS codes is studied. 3. A bilevel group network coding method on subgroup H based on second-order projective linear group PGL2, p) is proposed. It is proved that bilayer group network codes in group direct product H _ n can be constructed by using additive group Z _ p and Zp1 n-long linear codes. Finally, an example of matroid network is given to illustrate the advantages of the proposed coding scheme in the area of reachability.
【學(xué)位授予單位】：西安電子科技大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類號(hào)】：TN911.2;O157.5

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本文編號(hào)：1935976