几种常用纠错码的性能分析及应用研究

目录设计总说明Introduction1 绪论 12 数字通信系统及纠错码的基本概念 32.1 数字通信系统 32.1.1 数字通信系统模型 32.1.2 数字通信的特点 42.2 差错控制系统及纠错码 52.2.1 差错控制系统分类 52.2.2 纠错码的原理 72.2.3 纠错码的分类 93 线性分组码123.1 汉明码的构造原理123.2 线性分组码的编码133.2.1 监督矩阵143.2.2 生成矩阵153.3 线性分组码的译码164 循环码194.1 循环码原理194.1.1 码多项式的按模运算214.1.2 生成矩阵214.1.3 生成多项式234.2 循环码的编码244.3 循环码的译码254.4 BCH 码264.5 RS 码 275 卷积码285.1 卷积码的编码 285.2 卷积码的图解表示 295.2.1 树状图 295.2.2 网络图 305.2.3 状态图 315.3 卷积码的解析表示 325.4 卷积码的译码 335.4.1 大数逻辑译码 335.4.2 维特比译码 356 纠错码在移动通信中的应用 416.1 移动通信的概述 416.2 Turbo 码的基本原理 416.3 Turbo 码在移动通信中的应用 426.3.1 在 INMARSAT 移动卫星通信系统中的应用426.3.2 在 CDMA 多用户检测中的应用426.3.3 在第三代移动通信系统 IMT-2000 中的应用427 总结 44参考文献 45致谢 46华北科技学院毕业设计（论文）第 I 页几种常用纠错码的性能分析及应用研究设计总说明人类社会进入 21 世纪的今天，通信技术和信息产业的长期高速发展，不仅将我们带入了信息时代，并且深刻地影响和改变着我们的生活工作方式，各种通信方式的广泛应用已成为我们这个时代的显著标志，使人足不出户，真正感受到“小小地球村”的魅力。以数字化、光纤化、移动化、网络智能化和技术水平不断发展为特征的现代通信行业，将带领人们进入未来的信息世界。但通信技术始终面临着一个不可避免的问题，即如何不断降低误码率，提高通信质量。提高信息传输的可靠性和有效性，是所有通信工作者所追求的目标。纠错码是提高信息传输可靠性的一种重要手段现代通信系统中，它被用来提高信道传输的可靠性和功率利用率，因此它可以检测并纠正信号传输过程中引入的错误，抗干扰能力强，所以纠错码的设计是保证数据可靠传输的一个重要组成部分。伴随着信息时代的到来以及微电子技术的飞速发展，今天纠错码已不再单纯是一个理论上探讨的课题了，它已成为一门标准技术而被广泛采用，它也不再是致力于专门研究的专业人员才应掌握的一门科学，而成为从事通信、计算机、电子系统工程的有关工程技术人员都必需掌握的一门技术。它在通信系统中的应用是不容忽视的。这是该毕业设计研究的意义所在。1948 年，香农（Shanno）发表了具有里程碑意义的The Mathematical Theory of Communications（通信的数学理论） 一文，提出了信道编码定理和信源编码定理，开创了信息论这门崭新的学科，从而为在信息系统中实现高效可靠的信息传输奠定了理论上的坚实基础。在随后的 50 多年的时间里，几代数学家和工程师都在孜孜不倦地探索着逼近去逼近 Shannon 理论的理想界限。第一个线性分组码是由汉明(Hamming)在1950 年发现的，它能纠单个错误。1954 年 Golay 发现 Golay 码，Reed 和 Muller 发现了 RM 码，1960 年，Bose、Ray-Chaudhuri 和 Hocquenghem 发现了能纠正多个错误的BCH 码，同年，Reed 和 Solomon 发现了多进制 RS 码。与线性分组码同时期提出的是卷积码。它最早由 Elias 于 1955 年提出，早期被称为树码（Tree Codes），现在称其为格图码（Trllis Codes）或卷积码。直到今天的 Turbo ,LDPC 码，所能达到的性能和Shannon 限间的距离被不断缩小。这些方法也已经投入到多个领域的商用中，如卫星通信和深空通信，数据存储，数据传输，移动通信，数字音频和视频传输等。纠错码无论在理论还是在实际中都得到飞速发展。 几种常用纠错码的性能分析及应用研究第 II 页现如今，纠错码已经成为一门标准技术被广泛应用。在通信领域中，CRC 校验已成为 CCT 对各类线路传输建议中必不可少的一部分；在移动通信中，纠错码被广泛用于模拟体制的信令传输及数字体制的整个传输，以提高传输的可靠性和节省珍贵频谱资源；在卫星通信中纠错码技术已成为用来降低对高功放的要求和减少地球站天线孔径的尺寸的经济可靠的方法，VSAT 和 VSAT 的兴起，都是和纠错码技术的应用有关的；在电话网上的数据传输中，纠错码、差错控制技术已是使高速数据传输成为现实的关键技术。纠错码技术还广泛应用于计算机存储和运算系统中，此外，纠错码技术还应用于超大规模集成电路设计中，以提高集成电路芯片的成品率，降低芯片的成本。该毕业设计研究的主要内容是介绍数字通信系统、纠错码的基本概念及其分类、以及几种常用纠错码的编译码原理、常用纠错码的应用领域研究及重要意义。几种纠错码包括线性分组码、循环码、BCH 码、RS 码、卷积码。这里对线性分组码、循环码和卷积码做了比较详细的介绍。通过对几种纠错码的分析后，我们再做进一步的研究，介绍一下纠错码在移动通信中的应用和发展。第一章说明纠错码的主要意义，第二章介绍了数字通信系统及纠错码的基本概念。接下来第三到五章是几种纠错码的研究，对其编译码原理分别进行讲解。第六章深入研究 Turbo 码在移动通信中的应用。主要介绍 Turbo 码在 INMARSAT 移动卫星通信系统中的应用、Turbo 码在 CDMA 多用户哦检测中的应用以及 Turbo 码在第三代移动通信系统 IMT-2000 中的应用。由 于 纠错码的内容非常丰富，涉及领域较广，所需数学知识较多、较深。而且篇幅、时间有限，这里不可能详细介绍所有内容，仅讨论纠错码理论中比较基本和重要的，并在实际应用中用得较多的各种码的编译码原理和方法。关键词差错控制；纠错码；编译码原理；移动通信华北科技学院毕业设计（论文）第 III 页Several commonly used error-correcting code performance analysis and in-depth studyIntroductionHuman society has entered the 21st century, communication technology and the rapid development of information industry term, not only us running into the information age, and profoundly affected and changed our lives work, various means of communication has become a widely used significant sign of the times, people stay at home, really feel the “small global village“ charm. To digital, fiber optic, mobile, network intelligence and technology is characterized by continuous development of the modern communications industry, will lead the people into the future world of information. However, communications technology has always been faced with an inevitable question of how to continue to reduce the error rate and improve communication quality. Improve the reliability of information transmission and the effectiveness of all communications workers in goal. Error-correcting code is to improve the reliability of information transmission is an important means of modern communication systems, it is used to improve the reliability of the channel and power transmission efficiency, so it can detect and correct signal errors introduced during transmission, anti-jamming ability, so the error-correcting code is designed to ensure reliable data transmission is an important part. With the advent of the information age and the rapid development of microelectronics technology, todays error-correcting codes is no longer simply a theoretical study of the subject matter, it has become a standard technology is widely used, it is no longer committed to specialized personnel may be acquired by a science and become engaged in the communications, computer, electronic systems engineering for engineering and technical personnel are required to master a skill. Its application in the communication system can not be ignored. This is designed to study the significance of graduation. In 1948, Shannon published the landmark “Mathematical Theory of Communication,“ a paper presented the channel coding theorem and the source coding theorem, pioneered information theory this new discipline, which in information systems to achieve efficient and reliable transmission of information to lay a solid theoretical foundation. In the ensuing 50 years time, generations of mathematicians and engineers are diligently 几种常用纠错码的性能分析及应用研究第 IV 页exploring the Shannon theory approach to approximate the ideal boundaries. The first linear block code is Hamming discovered in 1950, it can correct a single error. Golay code found in 1954, Reed and Muller found that the RM code, 1960, Bose, Ray-Chaudhuri and Hocquenghem found multiple errors to be corrected in the BCH code, the same year, Reed and Solomon found in multi-band RS code. With the same period of linear block codes convolutional codes is proposed. It was first proposed in 1955 by the Elias, early known as the Tree Codes, now called the grid graph code (Trllis Codes) or convolutional code. Until today, Turbo, LDPC codes can achieve the performance and the distance between the Shannon limit is shrinking. These methods have also been put into many areas of business, such as satellite communications and deep space communications, data storage, data transmission, mobile communications, digital audio and video transmission. Error correction code both in theory and in practice have been developed rapidly. Now, the error-correcting codes has become a standard technique is widely used. In the communication field, CRC check on the various lines has become a CCT essential part of the proposed transfer; in mobile communications, error-correcting codes are widely used in analog and digital signaling system, the entire transmission system in order to to improve transmission reliability and save precious spectrum resources; error-correcting codes in satellite communication technology has become used to reduce the demand for high-power amplifier and reduce the size of earth station antenna aperture economic and reliable method, VSAT and VSAT rise, are and error correction code technology is related to the application; the phone line data transmission, error correction codes, error control techniques to make high-speed data transmission is the key technology a reality. ECC technology is also widely used in computer storage and computing systems, in addition, error correction code technology is also used in VLSI design, integrated circuit chips in order to improve yield, reduce chip costs. The main graduation research is to introduce the digital communication system, the basic concepts of error-correcting codes and classification, as well as several common principles of encoding and decoding error-correcting codes, error-correcting codes commonly used in research applications and significance. Several error-correcting codes, including linear block codes, cyclic codes, BCH codes, RS codes, convolutional codes. Here for linear block 华北科技学院毕业设计（论文）第 V 页codes, cyclic codes and convolutional codes to do a more detailed description. Through analysis of several error-correcting codes, we do further research, introduce the error-correcting codes in mobile communication applications and development. The first chapter describes the main significance of error-correcting codes, the second chapter describes the error-correcting codes in digital communication systems and the basic concepts. The next five chapters is the third to the study of several error-correcting codes, respectively, to explain the principles of its codec. Chapter VI-depth study of Turbo codes in mobile communication applications. Introduceing the Turbo codes in INMARSAT mobile satellite communication systems applications, Turbo codes in CDMA multi-user detection Oh and Turbo codes in the third generation mobile communication system IMT-2000 applications. As the error-correcting code is very rich in content, covering a wider area, the necessary mathematical knowledge more deeply. And space, limited time, can not detail everything here, just discussing the theory of error-correcting codes more basic and important, and was used more in the practical application of various principles and codes of encoding and decoding methods. Key words: Error control；Error-correcting codes；Encoding and Decoding；Principle； Mobile Communications华北科技学院毕业设计（论文）第 1 页 共 46 页1 绪论当前人类已步入信息社会，通信是必不可少的。通信的目的是要把对方不知道的消息及时可靠的传送给对方，因此，要求一个通信系统传输消息必须可靠与快速，在数字通信系统中可靠与快速往往是矛盾的，若要求快速，则必然使得每个码元所占的时间缩短、波形变窄、能量减少，