Analysis And Research Of Polar Code Over Nonstationary Channels

Polar code is a new channel coding based on channel polarization.After the first launch of the polar code,it has attracted much attention in academia because it is the only one that has been proved to be capable of reaching Shannon's limit and has a low linear complexity.Although scholars around the world in the field of polar code have done a lot of researches and experiments,but its performance over nonstationary channel is still little exploration,this paper is about analysis and research of polar code over nonstationary channels.In fact,nonstationary channels are more common because nonstationary channels are more common in human social life and are difficult to control in a regular way.The study of polar code over nonstationary channel is beneficial to that it can be more commonly used in various aspects of life.In this paper,polar code will be researched over the nonstationary channel,and,the result is that the phenomenon of polarization still exists and a proof will be given.The specific research contents and results are as follows:(1)The implementation of polar code over stationary channels.The implementation of polar code is based on selecting stationary channels BEC and BSC.The process of polar coding and decoding and a method for constructing polar code over different channels were researched,which was the basis of research for polar code over nonstationary channels.The obtained results showed polarization figures and code performance figures.(2)Theoretical proof for polarization over nonstationary channels.Mathematical proof was done by advanced mathematics and probabilistic,according to link rule,symmetric capacity keeps unchanging,which made channel polarization over stationary channels deducted to nonstationary channels.At last,the whole proof process would be completed.(3)The research of polar code over nonstationary channels.This section is divided into three parts.Firstly,the appropriate nonstationary channel model,whose transfer probability is subordinate to the distribution of sine function in this paper,would be chosen.Then an experiment would be tested by setting different parameters separately.Secondly,the construction method and algorithm of polarization code were studied and improved,because the algorithm and construction methods of polar code over stationary channels were not suitable for nonstationary channels.Lastly,Monte Carlo method was used as the construction method,and the decoding algorithm of the polar code was improved by setting decodinginitial parameters of probabilities into the first layer function of decoding decision.After the polarization figure and code performance figure were obtained,the conclusion was drawn by analyzing different parameters and channels.The results show that different nonstationary channels probability parameters have different degree of polarization phenomenon.The code performance graph shows that the code performance over the stationary channels is better than that of the nonstationary channels.According to the mathematical proof and experimental verification,it is proved that the construction of polar code over nonstationary channels is feasible and the code has been polarized.However,the polarization phenomenon and the code performance over stationary channels are better than nonstationary channels.Based on the polarization code under the smooth channel,this paper analyzes and studies the polarization code over nonstationary channels,which provides a powerful guarantee for the future research and application of polar code over nonstationary channel.