Research On Polar Codes And Its Application In Communication Systems

Polar Codes has been selected into the 5G standard recently,and it has been only ten years since Arikan invented Polar Codes.There are a lot of scholars studying Polar Codes and a great number of papers has been put forward.Polar Codes is a error-correcting code which has been proven that can achieve channel capacity theoritically.Also Polar Codes has many advantages over others error-correcting codes.For example,Polar Codes has a simple structure,and has a low-complexity encoding&decoding algorithms,and has a good error-correcting ability and so on.Based on Channel Polarization,which is different from traditional error-correcting codes,there is a tight connection between Polar Codes and the Channel Polarization phenomenon.Polar Codes also has some features from G_N-coset code.The thesis begins to introduce Polar Codes from the basics.The thesis firstly introduces the Channel Polarization phenomenon,which is the ori-gin of the Polar Codes.There are two basic aspects of Channel Polarization,Channel Combining and Channel Splitting.The thesis reviews both aspects,respectively,then in-troduces the recursive Channel Polarization phenomenon.Also the thesis reviews some theroms of Polar Codes which are the fundamentals of Polar Codes.G_N-coset code is introduced,based on which the notion of Polar Codes is given.After that some related theroms are introduced in this thesis.How to construct Polar Codes is presented in this thesis.Since Polar Codes is a G_N-coset codes,the problem of constrcting Polar Codes is divided into two sections,how to get the generation matrix G_Nand how to select the infomation bit positions.Based on the recursive structure,the procedure of constructing the generation matrix G_Nis given.The method of selecting infomation bit position is also given.The decoding algorithm is introduced after the encoding of Polar Codes.The de-coding algorithm of Polar Codes is based on the SC decoding.So SC algorithm is firstly introduced.Then the thesis reviews the SCL and SCL-CRC decoding algorithm,which both are based on SC algorithm.In order to reduce the storage complexity of SCL-CRC algorithm,a parity-check aided SCL-CRC algorithm is given,which reduced the storage complexity at the cost of decoding performance.There are many channel models to describe the real channels,for example the AWGN channel,the fading channel,the burst noise channel,ect.The thesis looks into the Polar Codes on burst noise channel,and put forawrd a channel model with the help of a random interleaver.A method of contructing Polar Codes is given based on the channel model which is given in this thesis.Numberical results and analysis are also given in this thesis.