Research On Gaussian Approximation Construction And Decoding Algorithms For Polar Codes

Polar codes based on channel polarization theory are a kind of channel encoding technology,because it theoretically proved to achieve the Shannon limit,and have a definite structure and low complexity,thus polar codes have become the research focus of communication field so far.The channel polarization operation makes the N independent copies of a given binary discrete memoryless channel(B-DMC)to be transformed into N channels with a polarization effect by using the channel combining and splitting.Polar codes have been received considerable attention by many scholars since it is discovered by E.Arikan in 2009.And the polar codes have been preliminarily used in communication system.Although it is proved that polar codes can achieve the Shannon limit,the decoding performance of the polar codes with finite-length is not good enough compared with Low Density Parity Check codes.Therefore it is necessary to investigate the technology of polar codes.This thesis mainly focuses on the construction methods and decoding algorithms of polar codes over the binary erasure channel(BEC)and additive white Gaussian noise(AWGN)channel.The main contents of this thesis are summarized as follows.1.This thesis describes the channel capacity transition in the process of the channel combining and splitting.The encoding process of polar codes using the generating matrix is described,and the complexity of the encoding process is analyzed.2.BEC construction method,Monte Carlo construction method and Gaussian approximation construction method for polar codes over BEC and AWGN channel are investigated in detail.The improved Gaussian approximation construction method and simulation implementation of these construction methods are given.The simulation results show that,polar codes with the longer length constructed by the improved Gaussian approximation method have a better decoding performance compared with Gaussian approximation construction method.3.Based on making a detailed analysis of the Successive Cancellation(SC)decoding algorithm and the Belief Propagation(BP)decoding algorithm for polar codes,the Soft Cancellation(SCAN)decoding algorithm of the polar codes and simulation implementation of these decoding algorithms are given.The simulation results show that SCAN decoder has the faster convergence speed and better decoding performance with lower complexity compared with the BP decoder,and the polar codes with SCAN decoding algorithm have better decoding performance compared with the SC decoding algorithm.