Research Encoding And Decoding Of Polar Codes Under High Order Modulation

With the increasing demand of bandwidth on wireless communications, high order modulation has been a neccessary technology to improve the throughout of the transimission. On the other hand, the channel coding is an essential technology to ensure the error free transmission of information. Therefore, the joint design of coding and modulation in the communication transmission has attracting a lot of research interests. In the aspect of channel coding, polar codes have been a hot research topic because of its rich algebraic structure and excellent coding performance. The thesis mainly focuses on designing polar codes based on Gray mapping high-order modulation. By dividing the high order modulation into multiple parallel binary input channels with fixed transmission power, the construction of polar codes with high order modulation can be realized based on the method of the binary input channels.Chapter one describes the development of modern mobile communication channel coding and gives an overview of the research background and the history of polar codes. In the following, the chapter focuses on the state-of-the-art of the research of polar codes. Finally, the main research contents in the thesis are given.In the second chapter, the theory of polar codes is introduced in detail. In this chapter, we describe the channel polarization, the polar encoding process and the decoding algorithm called successive cacellation(SC). Finally, two improved decoding algorithms, namely, the list SC decoding algorithm and the stack SC decoding algorithm are introduced.In the third chapter, we mainly give several methods of the polar code construction. The principle and the operation steps of each method are described in detail. Finally, the complexity of the three methods under the SC decoding algorithm are analyzed and compared.The fourth chapter focuses on the design of polar codes on high order modulation with Gray mapping. First of all, the typical 8-PSK modulation is analysed. According to the intrinsic relations between the information bits and the constellation points, we propose a method of contructing polar codes with 8-PSK modulation with significant performance gain compared with the traditional one by simulation. Then, on the scenario of the 4-PAM(16-QAM as well) modulation, we also propose a similar method to contruct the polar codes. Finally The simulation result exhibits its advantage on the performance. Finally, we extend our study to more general modulation scenario, namely M-PSK/QAM. Two schemes on polar codes design in low SNR and high SNR in M-PSK/QAM are proposed respectively:(1). For the scenario of the high SNR, the information in the worst two equivalent channels is encoded and transmitted while one in other channels is directly transmitted without encoding. According to the simuation, the performance can be significantly improved;(2). For the scenario of the low SNR, the encoding in the worst three channels are taken into account. The simulations with various length of the codes show that the proposed scheme can bring greater encoding gain.The final chapter concludes the thesis and gives the next meaningful research direction.