Constructing Of Polar Codes For Arbitrary Length

In 2016,polar codes were successfully incorporated into 5G standard as the coding scheme of control channel in eMBB scenario.This indicates that the polar codes proposed by Pro-fessor E.Arikan will play an important role in 5G communication.Polar have been proved theoretically to be capable of achieving channel capacity and its coding and decoding com-plexity is very low,therefore,polar will play an increasingly important role in the field of communications.In the practical application of polar codes,there are still many problems to be solved,among which the problem of rate adaptation is particularly important.Because the length of polar codes is fixed to the power of 2,it does not have the arbitrary code length characteristics such as LDPC,when the information bit length is fixed,the length of polar codes can not be adjusted according to the bit rate.In the past,the method to solve this problem is puncturing,which can achieve arbitrary length without losing certain performance.A method of constructing arbitrary length polar codes based on power decomposition?PD?is proposed in this paper.This method decomposes arbitrary length polar codes into several standard polar codes.The error probability of each channel is calculated according to the code length and channel parameters of each block.The reliability of the whole polar codes is selected from all channels of each block according to their reliability ranking.The polar codes are coded and decoded separately according to the result.This paper provides a theo-retical basis for selecting the optimal channel of K as the information bits.This paper also focuses on the decoding method,parallel decoding is performed according to the coding char-acteristics.After decoding,the path of each block is combined to get the decoding result and then CRC check is performed.In addition,the computational complexity of the path com-bination method at the decoder side increases exponentially when there are more blocks,this paper proposes an improved combination algorithm,which retains h barpath after combining two sets of blocks.By this method,the computational complexity of path combination can be reduced from h^mto h²,in which m is the number of blocks.The polar codes constructed by PD can be computed in parallel during the encoding and decoding process,compared with the RCPP,the time complexity can be reduced.In this paper,several construction methods are exhaustively used to find the best SNR point,which is used to determine the construc-tion method of the coding.Finally,this paper simulates the arbitrary length polar codes and analyses its performance curve.The simulation results show that the performance of polar codes constructed by PD is slightly better than that of LDPC with the same code length 2304,when the bit error rate reaches10^-4,the performance gain is about 0.1dB.Compared with standard polar codes with code length 2048,when the frame error rate reaches 10^-3,the performance loss is about 0.1dB.When the code length is 640,the performance of PD polar codes is almost the same as that of quasi-uniform puncturing polar codes.In addition,with the increase of code length,the performance curve of the polar codes constructed by PD will show a jump.The closer the code length is to the maximum value in the combined code block?e.g.512,1024,2048?,the better the performance will be.Generally speaking,this method is simpler,more flexible and more systematic,and the gains of these advantages do not cause significant performance losses.