Research On Polar Codes Design Theory And The Applications In Signal Transmission

Polar codes have recently been adopted as the coding scheme for the con-trol channels of 5G,which are based on the channel polarization and have been proved to achieve the capacity by the successive cancellation(SC)decoding.Meanwhile,polar codes are one of the frontiers of research in channel codes and the applications have broad prospects.The coding and decoding theory of polar codes and the communication systems design based on the channel polar-ization are both the promising researches in the field of polar codes.However,the theory of analyzing the performance limits and the decoding performance of polar codes requires to be improved.Based on the theoretical performance,the practical polar-coded transmission systems with modulation and precoding need to be further studied.On this context,we research the polar codes de-sign theory and the applications in high-order modulation and MIMO systems to improve the performance of polar-coded transmission systems and guide the optimization of radio technology of wireless communication.In this dissertation,we first study the basic theory of polar codes and es-tablish the analysis framework for theoretical performance of polar codes so as to explore the performance limits.Then,based on this framework,we re-search the applications of polar codes in signal transmission using modulation and precoding.Meanwhile,we propose the practical polar-coded modulation(PCM)schemes and design the unitary precoding for polar-coded MIMO sys-tems,which enhance the practical potential of polar codes in the next generation wireless communication systems and improve the overall performance of the communication systems.In particular,this dissertation includes the following four aspects of innovative work:1)We focus on the MWDs of polar codes and concatenated polar codes to analyze the performance and optimize the encoding structure.In order to enu-merate all the codewords belonging to the MWD,the sphere constraint property is applied,which means that the codewords with the identical Hamming weight are distribute on a spherical shell.Based on this,two enumeration methods are proposed in this dissertation.We first propose a sphere constraint based enu-meration method(SCEM)to analyze the MWD of polar codes.Then,according to the SCEM and the Plotkin's construction of polar codes,a sphere constraint based recursive enumeration method(SCREM)is proposed to recursively cal-culate the MWD with a lower complexity.The enumeration results show that the proposed methods has about lower complexity compared with the existing methods.2)We design the high-performance decoding algorithm and explore the performance limits of short polar codes.We first propose the CRC aided sphere decoding(CA-SD)algorithm to achieve the maximum likelihood(ML)perfor-mance of CRC-polar concatenated codes.In the CA-SD,we transform the un-derlying parity check relationships in CRC as the equivalent new forms by em-ploying the Gaussian elimination method.That ensures the parity check bits can be uniquely judged by previous decoded bits rather than the redundant search during the CA-SD.By this means,the complexity of CA-SD is reduced.Then,we find that the ML performance of a simple CRC-polar concatenated scheme can approach the normal approximation of the finite blocklength rate.To op-timize the CRC-polar concatenated codes,we propose a parity-check SCEM(PC-SCEM)to analyze the MWD of concatenated polar codes by introducing the parity-check equations of outer codes.To reduce the complexity of CA-SD,we propose the CRC-aided hybrid decoding(CA-HD)algorithm,which is a combination of the adaptive successive cancellation list decoding and the CA-SD.The simulation results show that CRC-polar concatenated code under CA-HD with codeword length 128 and code rate 0.5 can achieve within about 0.025dB of the normal approximation of the finite blocklength capacity at the block error rate 10-3.3)We study agile construction scheme for PCM.In particular,we propose flexible rate-filling methods for both the multilevel coding based PCM(MLC-PCM)and the bit-interleaved PCM.In the MLC-PCM scheme,we show that the bit indices within each component polar code can follow a fixed,precomputed ranking sequence(e.g.,the Polar sequence in the 5G standard)while their allo-cated rates(i.e.,the number of information bits of each component polar code)can be fast computed by exploiting the target sum rate approximation and prop-er rate-filling methods.In the BIPCM scheme,the proposed method makes full use of the nesting structure of polar codes.Hence,BIPCM can be constructed by properly allocating the rates of each polar subcode.To allocate the rates of the component polar codes(or the polar subcodes),we propose two rate-filling methods based on the capacity and the rate considering the finite blocklength effect.Simulation results show the proposed fast construction method performs independently of the actual channel condition and is robust to diverse modula-tion and coding schemes in the 5G standard.4)The design of polar precoding for polar-coded MIMO(PC-MIMO)sys-tems is based on the idea of channel polarization.In contrast to the traditional design of MIMO precoding criteria,the proposed polar-precoding scheme relies on the polarization criterion.In particular,the precoding matrix design com-prises two steps.After selecting a basic matrix for maximizing the capacity in the first step,we design a unitary matrix for maximizing the polarization effect among the data streams without degrading the capacity.Moreover,the optimal polar precoding of the PC-MIMO system is derived under the polarization cri-terion and a method to design the polar precoding codebook is proposed based on the DFT precoding.Our simulation results show that the proposed polar-precoding scheme outperforms the state-of-the-art DFT precoding scheme.In this dissertation,we study the basic theory of polar codes and the extend the channel polarization into signal transmission.For polar codes,we propose an enumeration method for accurately analyzing the MWD of polar codes and study the performance limit of short polar codes.For the polar-coded signal transmission,we research the construction method for polar-coded modulation and the precoding scheme for PC-MIMO systems.The above research contents improve the basic theory of polar codes,increases the spectral efficiency of polar-coded signal transmission and guide the performance optimization of the wireless communication system.