一般二值信源算术码码谱研究

发布时间：2017-12-28 05:13

本文关键词：一般二值信源算术码码谱研究　出处：《西北农林科技大学》2016年硕士论文　论文类型：学位论文

【摘要】：分布式算术码是一种扩展的算术码,其对于短数据块表现出优良的性能,因其自身的优势得到广泛的应用。目前关于分布式算术码的研究,特别是关于其编码效率及解码复杂度的成果还相对较少。而算术码码谱能有效提高分布式算术码的编码性能并降低解码复杂度,对分布式算术码研究工作的进一步开展有重要的指导意义。但是算术码码谱现有的研究成果是基于二值等概信源提出的,大大限制了算术码码谱的应用范围。因此,本文在现有算术码码谱研究成果的基础上,将算术码码谱推广到二值非等概信源,以拓宽码谱的使用范围;并提出一种基于码谱数值算法的改进算法以提高计算效率,另外也给出了一种算术编码器的改进方案。本文具体研究内容如下:(1)算术编码器的改进。经典的算术编码器在编码结束时会在编码码流后面追加多个比特位,而且追加的比特位是没有限制的。本文提出一种改进的编码方式,即在编码结束时,追加比特位的工作放在解码端完成,其追加的比特位是有限制的,只需追加(01?)或者(10?)即可。理论以及实验结果表明优化后的编码方式既能保证编码结果落在最终的编码区间,同时也减少编码端的工作量,提高编码效率。(2)码谱数值算法的改进。算术码码谱的计算是个很复杂的问题,一般采用数值模拟算法来实现,该过程是迭代的,时间复杂度很高。本文提出一种改进算法,通过去掉多余的函数,精简数值算法,降低时间复杂度。本文从理论上证明了该改进算法的正确性,并通过实验验证了该改进算法的有效性,实验表明改进后算法的效率有10%~30%的提高。(3)基于二值非等概信源的算术码码谱研究。本文定义了二值非等概信源的初始谱形式,利用傅里叶变换得出了初始谱的一般显式解,并定义了谱进化规则以及最终谱。另外本文也定义了膨胀因子,以用来衡量解码过程的复杂度。在研究过程中,二值非等概信源的算术码码谱的计算采用改进后的数值模拟算法。最后,本文分析了二值非等概信源算术码码谱的基本性质以及特点,并通过实验验证了所述理论推理的正确性。
[Abstract]:Distributed arithmetic code is an extended arithmetic code, which shows good performance for short data blocks, and has been widely used because of its own advantages. At present, the research on distributed arithmetic code, especially on its coding efficiency and decoding complexity, is relatively small. The arithmetic code spectrum can effectively improve the coding performance and reduce the decoding complexity of distributed arithmetic codes, which has important guiding significance for the further research of distributed arithmetic codes. However, the existing research results of the arithmetic code spectrum are based on the two values, which greatly limit the application range of the arithmetic code spectrum. Therefore, based on the existing arithmetic code spectrum on the basis of research results, the arithmetic code spectrum applied to the two value of non equal probability source, to broaden the scope of the code spectrum; and put forward a kind of improved algorithm to improve the computing efficiency based on spectrum code numerical algorithm, and an improved scheme arithmetic coder is also given. The main contents of this paper are as follows: (1) improvement of arithmetic coder. The classical arithmetic coder will add more bits after the code stream at the end of the code, and the appended bits are not limited. This paper proposes an improved coding method, that is, at the end of encoding, the task of adding bits is placed at the decoder end, and the appended bits are limited, which only needs to be added (01?) or (10?)? Theoretical and experimental results show that the optimized coding method can not only guarantee the coding result falling in the final coding interval, but also reduce the workload of the coding end and improve the coding efficiency. (2) improvement of the numerical algorithm for the code spectrum. The calculation of the arithmetic code spectrum is a very complicated problem, which is usually realized by numerical simulation algorithm. The process is iterative and the time complexity is very high. In this paper, an improved algorithm is proposed to reduce the number of numerical algorithms and reduce the time complexity by removing redundant functions. In this paper, the correctness of the improved algorithm is proved theoretically, and the effectiveness of the improved algorithm is verified by experiments. Experiments show that the efficiency of the improved algorithm is improved by 10%~30%. (3) the study of the arithmetic code spectrum based on the two value non - equal information source. In this paper, we define the initial spectral form of the two valued non equal probability source. We get the general explicit solution of the initial spectrum by Fourier transform, and define the spectrum evolution rule and the final spectrum. In addition, the expansion factor is also defined to measure the complexity of the decoding process. In the course of the study, the arithmetic code spectrum of the two value non - equal information source is calculated by the improved numerical simulation algorithm. Finally, this paper analyzes the basic properties and characteristics of the two value non - equal source arithmetic code code spectrum, and verifies the correctness of the theoretical reasoning by experiments.
【学位授予单位】：西北农林科技大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TN911.21

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