Construction And Analyses Corresponding Performance Of Polar Codes In Wireless Channels

Polar codes, proposed by Arikan, are new channel codes based on channel polarization, they can achieve channel capacity of binary-input discrete memoryless channel(B-DMC) with low encoding and decoding complexity. They are expected to become new error correction methods in the future communications. In this thesis, we study the construction of Polar codes and puncturing Polar codes in wireless channels.The constructions of Polar codes and their corresponding performance in wireless communications are presented. Firstly, several constructions of Polar codes in additive white Gaussian noise(AWGN) channel are presented, and the performance are analysed in detail. Secondly, according to the characterisitics of Rayleigh channel, two construction methods of Polar codes are presented. For the case with channel with side information(CSI), the channel is equivalent to the block fading channel, and each fading block is regarded as Gaussian channel with constant gain. For the case with distribution information(CDI), the channel is equicalent to binary symmetric channel(BSC). Thirdly, the constructions of Polar codes of Rician channels both with or without side informationin, and modified BP decoding algorithm are discussed. The numerical simulations results show that the performance of Polar codes for Rayleigh channel with the side information is better than those codes with distribution information. For Rician channel, the performance of Polar codes is better than that with low density check parity codes(LDPC). In addition, the error bit performance decreases with the increase of Rician factor K. Furthermore, the performance of Polar codes with the side information is better than those without the side information.Considering the time-varying characteristics of the wireless channels, a novel puncturing scheme for Polar codes based on the reliability is proposed in the thesis. The posteriori probability is used as the reliability for each bit-channel, where the Gaussian approximation is used to give the estimations. The numerical simulation results show that the puncturing scheme in AWGN channel has a better performance than those with random and stopping-tree puncturing schemes. Moreover, an improved random puncturing scheme with systematic Polar codes is presented where the puncturing bits are selected randomly in the check set of systematic Polar codes. The simulation results show that this scheme has a better performance than those of random puncturing and improved random puncturing scheme of non-systematic Polar codes. In addition, the performance of the improved puncturing scheme increases greatly with the increase bit rate.