喷泉码与极化码的改进及应用

发布时间：2018-03-11 03:31

本文选题：喷泉码　切入点：极化码　出处：《华南理工大学》2014年博士论文　论文类型：学位论文

【摘要】：在现代社会中伴随着互联网技术和无线通信技术的快速发展，各式各样的数据均能够通过数字通信系统方便、快捷、完整地传输至世界各地。为了保证数字通信系统在传输过程中的可靠性，纠错码技术的改进研究受到人们的高度重视。线性分组码就是纠错码的一种主要类型，近十年间出现的新型线性分组码正逐渐引领着纠错码技术的改革和突破，它们的不断发展和完善势必会在未来数字通信中发挥至关重要的作用。新型线性分组码主要包括：喷泉码、极化码，他们的出现是纠错码领域在新世纪的一项重要成果。对于喷泉码，通过度分布函数进行有选择限制的编码，然后进行广播式的转发，当译码器接收到固定数量的编码码字后，就能够成功恢复信源信号，此过程由于其灵活的码率形式和较高的性能而得到青睐。基于信道极化理论的极化码，构造编码过程主要采用巴氏参数或是传输信道量化。极化码构造编码的关键点是：通过巴氏参数迭代或是传输信道量化公式简化计算，得到衡量信道可靠性的估计值，再进行虚拟信道的筛选。其根本在于如何迅速而精确地计算虚拟信道的可靠程度，构造所使用的算法偏离实际信道越少，其计算信道可靠性准确度就会越高，所构造极化码的性能也就越好。首先，本文改善喷泉码的译码算法，同时分析构造极化码时巴氏参数的性能，提出更适应于其他二进制对称信道极化码的构造方式，最后，提出极化码在中继信道和无线光通信系统中的应用。本文的主要贡献包括： 1.介绍当前新型线性分组码：喷泉码、极化码，并对他们的技术背景和发展现状进行了详细的分析、归纳与总结。基于不同喷泉码度分布函数的特殊构造，得到喷泉码的编译码特征和性质。另外，通过分析极化信道的聚合和分离的数字特性，定义连续删除译码算法的判断标准，得到极化码的编译码特征和性质。从而给出现有新型线性分组码之间的相互关系，并指出他们目前存在亟须解决的关键问题和解决建议。 2.提出喷泉码的优化部分译码方式。针对短码长的LT码，介绍了传统的置信度传播译码算法和高斯消元译码算法的应用，分析传统译码法存在的优缺点，将他们的优势选择合并，提出可应用于喷泉码的快速置信度传播译码算法。同时，还证明了快速置信度传播译码算法是LT码的最优化译码算法之一。此算法不仅提高了置信度传播算法的译码成功概率，而且其独特的排列译码方式，能够减少了译码的时延和对数据存储的需求。通过仿真结果可知，在二进制对称信道中，快速置信度传播译码算法比置信度传播译码算法的成功率至多提高了48.09%。在仿真时间方面，LT码的快速置信度传播译码算法所用的时间少于高斯消元译码算法但略高于置信度传播译码算法，同时存在一个时间平台的阈值。所以在短码长和低码率LT码传输过程中，快速置信度传播译码算法优于传统算法。 3.证明错误指数函数和极化码巴氏参数存在特定的上下界。首先，从错误指数函数的定义入手，分析在二进制无记忆对称信道中，以信道容量为变量域，错误指数函数及其辅助函数在二进制差错信道和二进制对称信道下具有极值的性质，进而提出二进制无记忆对称信道的极值定理。通过辅助函数，将此极值关系扩展至极化码编译码的巴氏参数当中，并证明当信道容量为变量域时，极化码编码后虚拟信道的巴氏参数也存在类似上下界关系。我们推断出在构造极化码过程中，估计虚拟信道的可靠性时应该关注二进制差错信道和二进制对称信道巴氏参数的数值。理论上，通过分析这两个信道的传输可靠性，我们能够重新构造可应用于其它信道的最优极化码方案。 4.提出基于极化码下界的一系列编码构造算法。以巴氏参数的极值定理为基础，通过分析巴氏参数和极化码构造时的性质，给出极化码迭代算法中，欠可靠信道的巴氏参数更为精确和更为收敛的下界。将此下界公式应用于极化码对虚拟信道可靠性的估计，对极化码欠可靠信道的构造方法进行改进和优化，提出适合于二进制对称信道的极化码构造算法，较传统巴氏参数迭代的估计更为准确，使得极化码的性能有小幅提升。而针对高斯白噪声信道，提出线性构造算法，并通过仿真得出参数选择的方案。 5.将极化码应用于半双工中继信道。由于极化码存在信道聚合与分离的特性能够在中继节点中转发，所以极化码能够在中继信道中得以应用。针对在半双工中继系统中，我们分析其模型及各节点的特性，基于译码转发协议与系统中传输向量的正交性，提出一个适合于极化码的构造及传输策略。同时，证明极化码在半双工中继信道中能够达到香农限信道容量的定理。我们提出对半双工系统中时分和码分参数的优化方案，以及说明随机编码信息选择策略是最优中继策略。最后给出仿真结果与总结。 6.分析了极化码在带光学湍流的自由空间光通信系统中的错误概率及性能，其系统采用辐照强度调制和直接检测的光学调制方式构造，调制方式选用副载波二进制相移键控数字调制方式，系统的纠错码选用极化码。针对不同气候所产生的大气湍流，，我们主要考虑强湍流条件下的Gamma-Gamma湍流信道模型。在位逐位交织信道中，配对错误概率将能够有效而准确地表示虚拟信道中序列的传输，同时还能够求出有渐近性的配对错误概率。在准静态衰落信道条件下，不同帧内的信号所受衰落是相互独立的，在其基础上，研究极化码误帧率性能存在的上界与下界，我们采用两种方法：巴氏参数估计法和密度演化估计法，其中，密度深化的估计方法得到的结果更加精确。仿真的数据结果说明在自由空间光通信系统中，极化码的应用能够改进系统的性能。总体来说，针对上述提出的算法，论文都通过软件仿真、测试及与传统算法的比较来验证其有效性和先进性。针对所有提出的定理，论文通过严格的数学推导证明，说明定理存在的严谨性及适用范围。
[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.

【学位授予单位】：华南理工大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TN911.2

【参考文献】