| Polar code is the only channel coding technology that can theoretically be proved to reach the Shannon limit and has excellent decoding performance.Puncturing is one of the main schemes to realize the rate compatibility of polar codes.Through puncturing,we can obtain the polar codes with flexible code length and variable code rate.The traditional puncturing algorithm has high complexity due to channel reconstruction,but the existing polar code puncturing algorithm without reconstruction does not consider the impact of puncturing and the distribution characteristics of the polarization channels,resulting in poor performance.Aiming at the existing problems,this paper proposes a polar code puncturing algorithm based on Gaussian approximation,a polar code puncturing algorithm based on channel difference,and a polar code puncturing algorithm based on two segments,respectively,from the channel construction,initial value of channel and characteristics of polarization subchannels.The main work and innovations include:1.In view of the traditional puncturing algorithm does not consider the channel degradation caused by puncturing,a polar code puncturing algorithm based on Gaussian approximation is proposed.Firstly,based on the investigation of Gaussian approximation construction,the Gaussian correction factors are introduced to derive the improved Gaussian approximation function.Then,the channel capacity in the channel polarization is analyzed,and the mapping relationship of channel capacity from the incapable bit to the puncturing bit are proposed.Finally,combined with the improved Gaussian approximation construction and channel capacity mapping,a polar code puncturing algorithm based on Gaussian approximation is proposed.Finally,the bit error rate performance of polar code puncturing algorithm based on Gaussian approximation is analyzed and verified by experiments.2.Aiming at the differential effect of puncturing on channels,a polar code puncturing algorithm based on channel difference is proposed.Firstly,it analyzes the difference of each channel caused by puncturing,deduces the probability of each channel being punctured and the probability of being set as the incapable bit,and gives the corresponding channel initial value expectation.Then,the puncturing bit vector and the incapable bit vector are proposed,and the transformation relationship between the puncturing bit vector and the incapable bit vector is given.Then,combined with channel differentiation analysis and channel initial value vector,a polar code puncturing algorithm based on channel difference is proposed.Finally,the bit error rate performance of polar code puncturing algorithm based on channel difference is analyzed and verified by experiments.3.According to the distribution characteristics of Log Likelihood Rate value in polarization subchannels,a polar code puncturing algorithm based on two segments is proposed.Firstly,according to the analysis of the distribution of Log Likelihood Rate value in channel polarization subchannels,the common of nonuniformity distribution of Log Likelihood Rate value in polarization subchannels is summarized.Secondly,through the analysis of the channel capacity,it is verified that the two segments selection strategy can effectively reduce the additional loss of channel capacity,and introduces the partial sum of Log Likelihood Rate values,and puts forward the specific strategy and selection conditions of two segment selection.Furthermore,based on the two segments strategy,a polar code puncturing algorithm based on two segments is proposed.Finally,the bit error performance of the puncturing algorithm and its improved puncturing algorithm are analyzed and verified by experiments. |
