本文選題：噴泉碼　切入點(diǎn)：極化碼　出處：《華南理工大學(xué)》2014年博士論文　論文類(lèi)型：學(xué)位論文

【摘要】：在現(xiàn)代社會(huì)中伴隨著互聯(lián)網(wǎng)技術(shù)和無(wú)線(xiàn)通信技術(shù)的快速發(fā)展，各式各樣的數(shù)據(jù)均能夠通過(guò)數(shù)字通信系統(tǒng)方便、快捷、完整地傳輸至世界各地。為了保證數(shù)字通信系統(tǒng)在傳輸過(guò)程中的可靠性，糾錯(cuò)碼技術(shù)的改進(jìn)研究受到人們的高度重視。 線(xiàn)性分組碼就是糾錯(cuò)碼的一種主要類(lèi)型，近十年間出現(xiàn)的新型線(xiàn)性分組碼正逐漸引領(lǐng)著糾錯(cuò)碼技術(shù)的改革和突破，它們的不斷發(fā)展和完善勢(shì)必會(huì)在未來(lái)數(shù)字通信中發(fā)揮至關(guān)重要的作用。新型線(xiàn)性分組碼主要包括：噴泉碼、極化碼，他們的出現(xiàn)是糾錯(cuò)碼領(lǐng)域在新世紀(jì)的一項(xiàng)重要成果。對(duì)于噴泉碼，通過(guò)度分布函數(shù)進(jìn)行有選擇限制的編碼，然后進(jìn)行廣播式的轉(zhuǎn)發(fā)，當(dāng)譯碼器接收到固定數(shù)量的編碼碼字后，就能夠成功恢復(fù)信源信號(hào)，此過(guò)程由于其靈活的碼率形式和較高的性能而得到青睞。基于信道極化理論的極化碼，構(gòu)造編碼過(guò)程主要采用巴氏參數(shù)或是傳輸信道量化。極化碼構(gòu)造編碼的關(guān)鍵點(diǎn)是：通過(guò)巴氏參數(shù)迭代或是傳輸信道量化公式簡(jiǎn)化計(jì)算，得到衡量信道可靠性的估計(jì)值，再進(jìn)行虛擬信道的篩選。其根本在于如何迅速而精確地計(jì)算虛擬信道的可靠程度，構(gòu)造所使用的算法偏離實(shí)際信道越少，其計(jì)算信道可靠性準(zhǔn)確度就會(huì)越高，所構(gòu)造極化碼的性能也就越好。首先，本文改善噴泉碼的譯碼算法，同時(shí)分析構(gòu)造極化碼時(shí)巴氏參數(shù)的性能，提出更適應(yīng)于其他二進(jìn)制對(duì)稱(chēng)信道極化碼的構(gòu)造方式，最后，提出極化碼在中繼信道和無(wú)線(xiàn)光通信系統(tǒng)中的應(yīng)用。 本文的主要貢獻(xiàn)包括： 1.介紹當(dāng)前新型線(xiàn)性分組碼：噴泉碼、極化碼，并對(duì)他們的技術(shù)背景和發(fā)展現(xiàn)狀進(jìn)行了詳細(xì)的分析、歸納與總結(jié)�；诓煌瑖娙a度分布函數(shù)的特殊構(gòu)造，得到噴泉碼的編譯碼特征和性質(zhì)。另外，通過(guò)分析極化信道的聚合和分離的數(shù)字特性，定義連續(xù)刪除譯碼算法的判斷標(biāo)準(zhǔn)，得到極化碼的編譯碼特征和性質(zhì)。從而給出現(xiàn)有新型線(xiàn)性分組碼之間的相互關(guān)系，并指出他們目前存在亟須解決的關(guān)鍵問(wèn)題和解決建議。 2.提出噴泉碼的優(yōu)化部分譯碼方式。針對(duì)短碼長(zhǎng)的LT碼，介紹了傳統(tǒng)的置信度傳播譯碼算法和高斯消元譯碼算法的應(yīng)用，分析傳統(tǒng)譯碼法存在的優(yōu)缺點(diǎn)，將他們的優(yōu)勢(shì)選擇合并，提出可應(yīng)用于噴泉碼的快速置信度傳播譯碼算法。同時(shí)，還證明了快速置信度傳播譯碼算法是LT碼的最優(yōu)化譯碼算法之一。此算法不僅提高了置信度傳播算法的譯碼成功概率，而且其獨(dú)特的排列譯碼方式，能夠減少了譯碼的時(shí)延和對(duì)數(shù)據(jù)存儲(chǔ)的需求。通過(guò)仿真結(jié)果可知，在二進(jìn)制對(duì)稱(chēng)信道中，快速置信度傳播譯碼算法比置信度傳播譯碼算法的成功率至多提高了48.09%。在仿真時(shí)間方面，LT碼的快速置信度傳播譯碼算法所用的時(shí)間少于高斯消元譯碼算法但略高于置信度傳播譯碼算法，同時(shí)存在一個(gè)時(shí)間平臺(tái)的閾值。所以在短碼長(zhǎng)和低碼率LT碼傳輸過(guò)程中，快速置信度傳播譯碼算法優(yōu)于傳統(tǒng)算法。 3.證明錯(cuò)誤指數(shù)函數(shù)和極化碼巴氏參數(shù)存在特定的上下界。首先，從錯(cuò)誤指數(shù)函數(shù)的定義入手，分析在二進(jìn)制無(wú)記憶對(duì)稱(chēng)信道中，以信道容量為變量域，錯(cuò)誤指數(shù)函數(shù)及其輔助函數(shù)在二進(jìn)制差錯(cuò)信道和二進(jìn)制對(duì)稱(chēng)信道下具有極值的性質(zhì)，進(jìn)而提出二進(jìn)制無(wú)記憶對(duì)稱(chēng)信道的極值定理。通過(guò)輔助函數(shù)，將此極值關(guān)系擴(kuò)展至極化碼編譯碼的巴氏參數(shù)當(dāng)中，并證明當(dāng)信道容量為變量域時(shí)，極化碼編碼后虛擬信道的巴氏參數(shù)也存在類(lèi)似上下界關(guān)系。我們推斷出在構(gòu)造極化碼過(guò)程中，估計(jì)虛擬信道的可靠性時(shí)應(yīng)該關(guān)注二進(jìn)制差錯(cuò)信道和二進(jìn)制對(duì)稱(chēng)信道巴氏參數(shù)的數(shù)值。理論上，通過(guò)分析這兩個(gè)信道的傳輸可靠性，我們能夠重新構(gòu)造可應(yīng)用于其它信道的最優(yōu)極化碼方案。 4.提出基于極化碼下界的一系列編碼構(gòu)造算法。以巴氏參數(shù)的極值定理為基礎(chǔ)，通過(guò)分析巴氏參數(shù)和極化碼構(gòu)造時(shí)的性質(zhì)，給出極化碼迭代算法中，欠可靠信道的巴氏參數(shù)更為精確和更為收斂的下界。將此下界公式應(yīng)用于極化碼對(duì)虛擬信道可靠性的估計(jì)，對(duì)極化碼欠可靠信道的構(gòu)造方法進(jìn)行改進(jìn)和優(yōu)化，提出適合于二進(jìn)制對(duì)稱(chēng)信道的極化碼構(gòu)造算法，較傳統(tǒng)巴氏參數(shù)迭代的估計(jì)更為準(zhǔn)確，使得極化碼的性能有小幅提升。而針對(duì)高斯白噪聲信道，提出線(xiàn)性構(gòu)造算法，并通過(guò)仿真得出參數(shù)選擇的方案。 5.將極化碼應(yīng)用于半雙工中繼信道。由于極化碼存在信道聚合與分離的特性能夠在中繼節(jié)點(diǎn)中轉(zhuǎn)發(fā)，所以極化碼能夠在中繼信道中得以應(yīng)用。針對(duì)在半雙工中繼系統(tǒng)中，我們分析其模型及各節(jié)點(diǎn)的特性，基于譯碼轉(zhuǎn)發(fā)協(xié)議與系統(tǒng)中傳輸向量的正交性，提出一個(gè)適合于極化碼的構(gòu)造及傳輸策略。同時(shí)，證明極化碼在半雙工中繼信道中能夠達(dá)到香農(nóng)限信道容量的定理。我們提出對(duì)半雙工系統(tǒng)中時(shí)分和碼分參數(shù)的優(yōu)化方案，以及說(shuō)明隨機(jī)編碼信息選擇策略是最優(yōu)中繼策略。最后給出仿真結(jié)果與總結(jié)。 6.分析了極化碼在帶光學(xué)湍流的自由空間光通信系統(tǒng)中的錯(cuò)誤概率及性能，其系統(tǒng)采用輻照強(qiáng)度調(diào)制和直接檢測(cè)的光學(xué)調(diào)制方式構(gòu)造，調(diào)制方式選用副載波二進(jìn)制相移鍵控?cái)?shù)字調(diào)制方式，系統(tǒng)的糾錯(cuò)碼選用極化碼。針對(duì)不同氣候所產(chǎn)生的大氣湍流，，我們主要考慮強(qiáng)湍流條件下的Gamma-Gamma湍流信道模型。在位逐位交織信道中，配對(duì)錯(cuò)誤概率將能夠有效而準(zhǔn)確地表示虛擬信道中序列的傳輸，同時(shí)還能夠求出有漸近性的配對(duì)錯(cuò)誤概率。在準(zhǔn)靜態(tài)衰落信道條件下，不同幀內(nèi)的信號(hào)所受衰落是相互獨(dú)立的，在其基礎(chǔ)上，研究極化碼誤幀率性能存在的上界與下界，我們采用兩種方法：巴氏參數(shù)估計(jì)法和密度演化估計(jì)法，其中，密度深化的估計(jì)方法得到的結(jié)果更加精確。仿真的數(shù)據(jù)結(jié)果說(shuō)明在自由空間光通信系統(tǒng)中，極化碼的應(yīng)用能夠改進(jìn)系統(tǒng)的性能。 總體來(lái)說(shuō)，針對(duì)上述提出的算法，論文都通過(guò)軟件仿真、測(cè)試及與傳統(tǒng)算法的比較來(lái)驗(yàn)證其有效性和先進(jìn)性。針對(duì)所有提出的定理，論文通過(guò)嚴(yán)格的數(shù)學(xué)推導(dǎo)證明，說(shuō)明定理存在的嚴(yán)謹(jǐn)性及適用范圍。
[Abstract]:In the modern society with the rapid development of Internet technology and wireless communication technology, every kind of data can through the digital communication system is convenient, fast and complete transmission to the rest of the world. In order to ensure the reliability of the digital communication system in the transmission process, improvement of the error correcting code technology has been paid more attention to.
One of the main types of linear block codes are error correcting code, linear block code model appeared in recent ten years is gradually leading the reform and breakthrough of the error correcting codes, their continuous development and perfection will play a crucial role in future digital communication. The new linear codes include: fountain codes, polarization code. They are in the field of error correcting code is an important achievement in the new century. For fountain codes, are selectively restricted by encoding degree distribution function, and then broadcast forward, when the decoder receives a fixed number of encoding code, you can restore the source signal successfully, this process is favored because of its performance flexible form and high rate. Based on the channel polarization theory of polarization code structure encoding process mainly adopts PAP or transmission channel parameters quantization. Polarization coding related codes The key point is: through the parameter iteration or PAP simplified calculation of transmission channel quantization formula, get the estimated value of the channel reliability measure, then screening virtual channel. It lies in the degree of reliability of how to quickly and accurately calculate the virtual channel, using the proposed algorithm from the actual channel is less, the calculation accuracy of the channel reliability will be higher, the structure performance of polarization code is better. Firstly, this paper improves the decoding algorithm of fountain codes, and performance analysis of structural parameters of the PAP polarization code, put forward more suitable for other known binary on the way, constructing a channel polarization code. Finally, proposed the application of polarization code in the relay channel and the wireless optical communication system in.
The main contributions of this article include:
The 1. introduces the current model of linear block codes: fountain codes, polarization code, and the technical background and development status of them were analyzed, classified and summarized. The special structure of different degrees of fountain codes based on distribution function by fountain codes characteristics and properties. In addition, through the analysis of the digital characteristics of polymerization and separation polarization channel, standard definition of continuous erasure decoding algorithm, polarization coding characteristics and properties. In order to have the relationship between model of linear block codes, and points out that they are the urgent need to solve the key problems and solutions.
2. optimize the partial decoding mode of fountain codes. For short LT codes, introduces the application of belief propagation decoding algorithm and decoding algorithm of the traditional Gauss elimination, analysis of advantages and disadvantages of traditional decoding method, their advantages will merge, proposed can be applied to rapid fountain codes belief propagation decoding the algorithm is proved. At the same time, the rapid belief propagation algorithm is one of optimization of LT decoding algorithm. This algorithm not only improves the decoding success probability of belief propagation algorithm, and its unique permutation decoding methods, can reduce the decoding delay and data storage requirements. The simulation result shows that in the binary system symmetric channel, fast belief propagation decoding algorithm to improve the rate of 48.09%. in the simulation time than belief propagation decoding algorithm of LT codes, fast belief propagation decoding The time spent in the algorithm is less than the Gauss elimination algorithm, but it is slightly higher than the belief propagation decoding algorithm. Meanwhile, there exists a time threshold. So in the short code length and low bit rate LT code transmission, the fast confidence propagation decoding algorithm is better than the traditional algorithm.
3. proved wrong exponential function and polarization parameters have upper and lower bounds on the specific code of PAP. First of all, starting from the definition of error index function, analysis of memoryless symmetric channel in the binary system, the channel capacity of variable domain, error index function and auxiliary function with extremal properties in binary error channel and binary symmetric channel, extreme value and then put forward the theorem of binary memoryless symmetric channel. Through the auxiliary function, the parameters of this pap extremum relationship extends to the polarization code, and it is proved that when the channel capacity of variable domain, polarization encoding parameters of the virtual channel after the PAP is similar to upper and lower bounds on the relationship. We infer that in the process of constructing polarization code should pay attention to the binary, numerical error channel and binary symmetric channel parameters estimation of the reliability of PAP virtual channel. In theory, through the analysis of the two letter The transmission reliability of the channel, we can restructure the optimal polarization code scheme that can be applied to other channels.
4. put forward a series of encoding algorithm of polarization code based on lower bound. In extreme value theorem based PAP parameters, through analysis of the properties and parameters of PAP polarization code structure, gives the polarization code algorithm, less reliable channel parameters of PAP is more accurate and more lower bound for the convergence. This formula is applied to the lower bound polarization code estimation of virtual channel reliability, improve and optimize the construction method of polarization code insufficient reliable channel, proposed algorithm to construct polarization code suitable for binary symmetric channel, compared with the traditional PAP iterative parameter estimation is more accurate, the performance of polarization code slightly improved. While the Gauss white noise channel, proposed algorithm linear structure, and the parameter selection scheme by simulation.
The 5. polarization code used in half duplex relay channel. The polarization characteristics of channel code aggregation and separation can be forwarded at the relay node, so polarization code can be used in the relay channel. In half duplex relay system, we analyze the characteristics of the model and each node, orthogonal vector decode and forward transmission protocol with the system based on the proposed a suitable polarization code structure and transmission strategy. At the same time, that polarization code in the half duplex relay channel can achieve the Shannon limit channel capacity theorem. We propose optimization scheme of time division half duplex system and code parameters, and random selection strategy is the optimal relay information encoding strategy. Finally simulation results are given and analyzed.
6. analysis of polarization code in free space optical communication systems with optical turbulence in the error probability and performance, the structure of optical modulation of irradiation intensity modulation and direct detection system, modulation subcarrier selection of binary phase shift keying digital modulation, error correction code system uses polarization code in atmosphere turbulence in different climate. Produced, we mainly consider the Gamma-Gamma turbulence channel model strong turbulence conditions. In the bitwise interleaving channel, matching error probability will be able to effectively and accurately represent the transmission sequence of virtual channels, but also can calculate the paired error probability asymptotics. In quasi-static fading channel under different signal frame by fading is independent of each other, on the basis of its upper and lower bounds of polarization code fer performance, we use two methods: Pap parameter estimation The method of estimation and density evolution estimation, in which the density estimation method is more accurate. The simulation data show that the application of polarization code in free space optical communication system can improve the performance of the system.
Overall, according to the proposed algorithm, thesis through software simulation, testing and comparison with the traditional algorithm to verify its effectiveness and superiority. For all proposed the theorem, through strict mathematical derivation proves that the rigor and applicability of theorem of existence.

【學(xué)位授予單位】：華南理工大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類(lèi)號(hào)】：TN911.2

【參考文獻(xiàn)】

相關(guān)期刊論文 前5條

1 岳殿武,徐澄圻;關(guān)于糾錯(cuò)碼的若干新方向[J];重慶郵電學(xué)院學(xué)報(bào)(自然科學(xué)版);2000年04期

2 黃誠(chéng);易本順;;基于拋物線(xiàn)映射的混沌LT編碼算法[J];電子與信息學(xué)報(bào);2009年10期

3 諶娟;柯熙政;程婷;;自由空間光多輸入多輸出系統(tǒng)中的差分空時(shí)碼[J];光學(xué)學(xué)報(bào);2013年02期

4 ;Intermedia-Based Video Adaptation System:Design and Implementation[J];Tsinghua Science and Technology;2012年02期

5 黃根全;;大氣湍流下無(wú)線(xiàn)光通信信道性能研究[J];西安工業(yè)大學(xué)學(xué)報(bào);2011年05期

本文編號(hào)：1596408