Information Bit Selection And Its Shortening As Well As Puncturing Design For Polar Codes

The Polar code proposed by Arikan in 2009 is the first kind of channel coding technology that can be proved theoretically to achieve channel capacity under general discrete memoryless symmetric channel conditions.Its decoding complexity is only only O(Nlog N),where N is the code length.Polar code has become the research focus in the field of channel coding after Turbo code and LDPC code.It has also been adopted as a kind of channel coding scheme by 5G communication technology standard.Polar code is capable of approaching the channel capacity by exploiting the channel polarization phenomenon over symmetric channel.An important step in the encoding procedure of polar codes is to pick out the channels with the highest reliability for information delivery,while those relatively non-reliable and unselected channels are frozen.If the channel is symmetric,the frozen channels can deliver all zero bits.Arikan presented a generic method to calculate the reliability of different polarized channels,which can effectively fulfill the polar code construction requirement over the binary erasure channel.Nonetheless,in the additive white Gaussian noise channel,the reliabilities of polarized channels can be assessed by employing Monte Carlo method,density evolution analysis and Gaussian approximation analysis.Monte carlo and density evolution analysis have the problems of high computational complexity,which make them difficult to be realized.While the Gaussian approximation algorithm is sensitive to noise.In this paper,we proposed an LLR criterion based construction method to estimate the reliabilities of different polarized channels.And numerical analysis and simulation results are presented to show that,the proposed LLR criterion based method provides us a simple but efficient method to accurately estimate the polarized channel reliability,and its advantage is the low realization complexity and the achieved superior performance.In practical communication system,it is often necessary to dynamically adjust the code rate according to the different channel conditions.Puncturing and shortening are two common techniques of rate compatible coding.The existing design methods of Polar shortening and puncturing include QUP method,hamming weight method based on information bit binary index and bit flipping method.In this paper,noiseless decoding analysis and logarithmic likelihood ratio criterion are used to select shortened bit indices and perforated bit indices according to the channel reliability ranking.The simulation results are presented to show that the proposed shortening and puncturing deisgn has the advantages of simple implementation with excellent performance.The results of the noiseless decoding analysis method and the logarithmic likelihood ratio criterion of Polar code information bit selection,puncturing and shortening design provide useful reference for the further research on Polar code information bit selection and rate-compatible coding design.