极化码构造与译码算法研究

发布时间：2017-12-26 21:08

本文关键词：极化码构造与译码算法研究　出处：《西安电子科技大学》2016年博士论文　论文类型：学位论文

更多相关文章： 极化码 信道极化 信道编码 信息论

【摘要】：极化码是基于信道极化现象提出的第一类被证明在码长无限长时可以达到二元对称信道容量限的信道编码技术。信道极化现象是指当码长无限长时,二元对称信道可极化为两类信道,一类是容量为0的纯噪声信道,另一类是容量为1的无噪信道,其中无噪信道所占比例为原始二元对称信道的信道容量。但是,当码长受限时,信道不能充分极化,会存在一些极化信道的容量小于1的情况,若在此类信道上传输1比特的信息将会发生错误译码。因此,与优化过的低密度校验码和Turbo码相比,有限长极化码的性能并不理想。此外,极化码的构造是与信道的统计特性相关的,且在二元删除信道下的构造比较简单,但在非二元删除信道下的构造较复杂。本文的主要工作是研究有限长极化码的构造和译码,以及非二元极化码的速率匹配和译码算法,主要包括以下四部分内容：基于LDPC码的高斯近似理论,提出了一种基于高斯近似的极化码构造方法。首先,采用高斯近似的方法估计每个子信道的错误概率,从而获得极化码误组率的精确表达式,在此基础上,以最小化误组率为目标,提出了一种基于高斯近似的极化码构造方法。复杂度分析表明,基于高斯近似的极化码构造方法的实现复杂度比蒙特卡洛方法和密度进化方法低,另外,采用高斯近似估计的极化码误组率与计算机仿真结果一致。为降低极化码的译码复杂度,研究了基于统计排序的译码方法,提出一种基于阈值的统计排序译码算法,可解决原始统计排序译码需要测试大量码字导致复杂度较高的问题。该算法基本原理是：通过给接收信号设定阈值,译码器在译码过程中仅翻转幅度小于阈值的硬判决比特,从而降低了需要翻转比特的个数,降低了测试码字的个数。通过复杂度和性能分析,可以预估给定阈值下平均需要测试的码字个数和高信噪比区域的性能。仿真表明短码时统计排序译码可以达到和列表译码同样的性能,对于中长码,需要更高阶的统计排序译码来达到更好的性能。此外,本文还研究了CRC辅助的统计排序译码算法,结果表明,高码率极化码采用CRC辅助的统计排序译码的性能优于CRC辅助的列表译码的性能,而低码率时的结果相反。提出了一种分段CRC辅助列表译码的译码算法,该算法通过对信息序列进行分段校验,可在译码过程中及时删除错误的路径,以使正确路径的分支得到更好的保留从而提高译码性能。分析和仿真结果显示,该算法以漏检概率为代价,降低了译码误组率和译码复杂度。针对非二元极化码输入符号集元素个数为合数时会产生多层极化现象,提出了一种多层极化速率匹配方法。为了进行误组率最低的速率匹配,先给出了多层极化码的误组率表达式,然后提出利用线性复杂度的元素交换算法代替指数复杂度的穷搜索方案来进行速率匹配方案搜索。虽然理论上不能证明元素交换算法得到的结果为全局最优解,但是仿真结果表明,在不同码率下,元素交换算法和穷搜索方法得到的结果一致。此外,本文还研究了多层极化码的逐次消除译码算法,以四元删除信道为例,将适用于二元信道的逐次消除译码算法推广到多层极化的非二元信道。
[Abstract]:Polarimetric code is the first kind of channel coding technology based on channel polarization, which is proved to reach two yuan symmetric channel capacity limit when the code length is infinitely long. The phenomenon of channel polarization is that when the length of code is infinite, the two element symmetric channel can be polarized into two kinds of channels, one is the pure noise channel with 0 capacity, the other is the channel with the capacity of 1, and the proportion of the noiseless channel is the original two yuan symmetric channel capacity. However, when the code length is limited, the channel can not be fully polarized, there will be some polarization channel capacity less than 1. If we transmit 1 bits of information on such a channel, we will have an error decoding. Therefore, compared with the optimized low density parity check code and Turbo code, the performance of the finite length polarization code is not ideal. In addition, the construction of the polarization code is related to the statistical characteristics of the channel, and the construction under the two element deleted channel is relatively simple, but the construction under the non two bit deleted channel is more complex. The main work of this paper is to construct and research of finite polarization decoding code, and the rate of two yuan non polarization code matching and decoding algorithm, mainly includes four parts: LDPC codes based on Gauss approximation theory, put forward a method for constructing the Gauss approximation method based on polarization code. First, we use the Gauss approximation to estimate the error probability of each sub channel, so as to get the exact expression of the error rate of the polarization code. On this basis, to minimize the error rate, we propose a method of constructing the polarization code based on the Gauss approximation. Complexity analysis shows that the polarization code construction method based on Gauss approximation implementation complexity than Monte Carlo method and the density evolution method is low, in addition, the Gauss approximation of polarization code group error rate and computer simulation results. In order to reduce the decoding complexity of polarization codes, a statistical ranking based decoding method is studied. A statistical ranking and decoding algorithm based on threshold is proposed, which can solve the problem of the complexity of the original statistical sorting and decoding, which requires a large number of codewords to be tested. The basic principle of the algorithm is that, by setting the threshold for the received signal, the decoder will only turn the hard decision bits smaller than the threshold in decoding process, thus reducing the number of bits to be turned and reducing the number of test codewords. Through the analysis of complexity and performance, the number of code words and the performance of high signal to noise ratio region can be estimated at a given threshold. Simulation results show that statistical sorting and decoding can achieve the same performance as list decoding. For medium and long codes, higher order statistical sorting and decoding are needed to achieve better performance. In addition, CRC aided statistical ranking and decoding algorithm is also studied. The results show that the performance of CRC aided statistical sorting decoding is better than that of CRC aided list decoding, while the result of low bit rate is opposite. A segmented CRC auxiliary list decoding algorithm is proposed. By segmenting the information sequence, the algorithm can delete the wrong path in time, so as to make the branch of the correct path better reserved and improve the decoding performance. The results of analysis and simulation show that the algorithm reduces the error rate of decoding and the complexity of decoding at the cost of missing detection probability. Two yuan for non polarization code input symbol set the number of elements for the number will be generated when the multi polarization phenomenon, a method is proposed for matching multi polarization rate. In order to achieve the lowest rate matching, we first give the expression of the misrepresentation rate of the multilevel polarization code, and then propose a linear complexity element exchange algorithm instead of the exponential complexity search algorithm to search for the rate matching scheme. Although it can not be proved theoretically that the result of element exchange algorithm is the global optimal solution, the simulation results show that under different code rates, the results obtained by element exchange algorithm and poor search method are consistent. In addition, we also study the successive elimination algorithm of multilevel polarization codes. Taking the four element deleted channel as an example, we apply the successive elimination algorithm applied to Yu Eryuan channel to the multilevel polarized non two channel.
【学位授予单位】：西安电子科技大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TN911.22

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