Research On Polar Codes Application

Polar Code is compared with the Reed-Muller Codes; from the principle and numerical Polar Code is a hot research topic in the area of error correcting codes recently. Itwas proved that the Polar Code achieves symmetric capacity of binary discrete channels with the code length going to infinity. Comparing to the traditional Low Density Parity Check Codes and Turbo Codes, Polar Codes present more structural characteristics and it is easier to analyze the codes’ error performance. Currently, there is an immense number of researches in Polar Code. This thesis mainly focus on the code application problems and the error performance, the improvement of Successive Cancellation List decoding algorithm and problem of polar code in wiretap channel.Firstly, the thesis reviewed the basic principle of channel polarization and the Posimulation results, the Reed-Muller codes can be substitute by the Polar Code in real engineering application. This thesis gives some polar code simulation results under the Successive Cancelation decoding algorithm and the message bits and frozen bits’ distribution in the vector 1; and analyzes the correlation between SC decoding algorithm and the finite length polar code structure.In Polar Code decoding process, the Successive Cancellation decoding algorithm consider the frozen bits as random variations, so the SC decoding is not an maximum likelihood decoding algorithm. It restricts the error performance of Polar Codes. The most promising improvement of SC decoding is the SC List decoding algorithm which preserve decoding path instead of only on path is preserved in SC algorithm. The performance of SCL is near to the ML bound when the number is very large. Code path can also be verified by CRC and a path can be selected by the criteria that passes the CRC check. The performance of SCL+CRC algorithm decoding surpass the ML bound and has a huge improvement with little lose on code rate. But the SCL algorithm multiples the computation complexity and the storage consumption of the decoding path.To improve the SCL algorithm, the thesis presents a multi-CRC SCL algorithm to reduce the storage consumption and compared the error performance of the algorithm to the SCL+CRC and the adaptive SCL+CRC.Moreover, the thesis discusses the application of Polar Code in the wiretap channel.In the degraded wiretap channel, Polar Code was proved to achieve the secrecy capacity.The thesis considers the problem of finite length Polar code in the wiretap model and researches the properties of the degraded wiretap channel, and then proposes a secret key distribution scheme. Then the secrecy is researched when the key used as the frozen bits of Polar Code.