Research Of Polar Code

Channel coding technology is an extremely pivotal technology in communication system.After Arikan put forward the concept of Polar Code for the first time,it has become an active channel coding research direction in recent years.Because of the excellent error correction performance and the regular with low complexity of the encoding/decoding structures,Polar Code has received wide attention by the code researchers.Although Turbo code and LDPC code have already been state-of-the-art techniques and widely used in a variety of communication systems,the error correction performance of Polar Code has outperformed them.However,the performance of Polar Code is not that good when the code length is finite.Therefore,it is necessary to carry out a large amount of research on the better performance of communication system,such as effective information bit channel selection which is according to the capacity difference of bit channels caused by channel polarization,efficient decoding algorithms and so on.In this paper,we start with the basic polarization principle of Polar Code.Firstly,we emphatically study a kind of key technique of Polar Code--Bit Channel Selection.We calculate Bhattacharyya parameter to explain the bit channel selection in BEC environment.The two influenced aspects of this method include that the channel transition probabilities and the code lengths.Density Evolution algorithm is focused on.For Density Evolution algorithm,there are lots of recursive convolution calculations in L domain and G domain respectively.Besides Density Evolution algorithm needs to constantly switch between the two domains while the convolutions are calculating and to maintain high dimensional vectors.But anyway it has universal applicability to binary-input discrete memoryless channel.Gauss approximation algorithm is with much lower complexity than Density Evolution algorithm.In this section,we also make a comparative analysis of Density Evolution algorithm and Gauss approximation algorithm.At the same time we find that Gauss approximation algorithm is not robust enough.We also provide an overview of channel detection,which is another bit channel selection method.Secondly,we introduce the encoding algorithm of Polar Code which is used by the regular butterfly linear tectonic architecture and the results of bit channel selection.Finally,we simulate the performances of the basic SC algorithm,SCL algorithm and CRC-SCL algorithm in AWGN environment and then the analysis results are given.The longer the code length is,the more obvious the polarization effect is;Under a fixed code length and a certain area of SNR,the increasement of reserved path number will improve the performance,however,when the number exceeds a critical value,there will be no significant improvement;The cyclic redundancy check bits play a significant role in improving the performance;For different decoding algorithms,the SCL algorithm is better than SC algorithm,the CRC-SCL algorithm is better than SCL algorithm.