带有记忆为1的二进制信道的零错误信道容量

发布时间：2019-04-08 17:17

【摘要】：信道容量问题是信息论中的一个核心问题,Shannon给出的信道编码定理是指,对于一个有噪声的信道,当信息的传输速率不大于信道容量时,通过增加传输序列的长度,可以使得传输的错误概率趋近于0。随着信息论不断的发展,人们意识到有一些信道是不能容忍传输错误(例如当只需要传输少量信息时),因此要求错误概率必须等于0,继而引出零错误信道容量这一概念。不同于经典的信道容量,零错误信道容量要求当信息的传输速率不大于零错误信道容量时,一定存在某种传输策略使得传输的错误概率等于0。零错误信道容量这一概念被提出后,相较于经典的信道容量,零错误信道容量对传输性能要求很高,同时也涉及到组合数学等其他知识,一直是一个很具有挑战性的问题,相关的研究进展很缓慢。因此,研究者们从对普遍结论的研究转向对特例的研究。其中一个最为简单的模型就是,带有记忆为1的二进制离散信道。在本文之前,已经有研究者计算出其中部分信道的具体零错误信道容量,或给出下界。本文首先阐述了有关零错误信道容量研究的进展,指出由于该问题的研究过于困难,因此在近几年的研究中,研究者们开始把研究重心转移到一些特定信道,其中包括化学信道,时间信道,以及本文所研究的带有记忆为1的二进制信道容量。然后对本文中将要运用的信息论基础知识予以阐述,继而详细罗列了有关带有记忆为1的零错误信道容量的已有研究结论。接着本文针对该模型下还未解决的问题进行研究,并计算出来了其中关键的六种信道所对应的零错误信道容量。最后利用包含与被包含关系,推出了其余所有的记忆为1的零错误信道容量,从而完成了对该模型的全部研究。
[Abstract]:The channel capacity problem is a core problem in the information theory. The channel coding theorem given by Shannon means that for a noisy channel, when the transmission rate of the information is not greater than the channel capacity, the length of the transmission sequence is increased by increasing the length of the transmission sequence. It can make the error probability of transmission approach to 0. With the development of information theory, people realize that some channels cannot tolerate transmission errors (for example, when only a small amount of information is needed), so the error probability must be equal to 0, and then the concept of zero error channel capacity is introduced. Different from the classical channel capacity, the zero error channel capacity requires that when the transmission rate of information is not greater than the zero error channel capacity, there must be some transmission strategy which makes the error probability of transmission equal to 0. Since the concept of zero error channel capacity has been proposed, compared with the classical channel capacity, the zero error channel capacity requires very high transmission performance, and also involves other knowledge such as combinatorial mathematics, which has always been a challenging problem. Progress in related research has been slow. As a result, researchers have shifted from the study of general conclusions to the study of special cases. One of the simplest models is a binary discrete channel with a memory of 1. Before this paper, some researchers have calculated the specific zero error channel capacity of some of these channels, or given the lower bound. In this paper, the research progress of zero error channel capacity is introduced firstly, and it is pointed out that the research on this problem is too difficult, so in recent years, researchers began to shift the research focus to some specific channels. These include chemical channel, time channel, and binary channel capacity with memory of 1. Then the basic knowledge of information theory to be used in this paper is described, and then the existing research conclusions about the capacity of zero error channel with memory of 1 are listed in detail. Then the unsolved problem under this model is studied and the zero error channel capacity corresponding to the six key channels is calculated. Finally, using the inclusion-inclusion relationship, all the other zero error channel capacities with memory of 1 are derived, and all the studies on the model are completed.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN911.2

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