Research Of Concatenation And Rate-Compatible Construction Method For Polar Codes

Polar codes are the first class of channel coding schemes that can be proved to achieve the capacity of binary symmetric channels.The basic principle of polar codes is to convert binary symmetric channels into two types.One is the noiseless channel with the capacity of 1 for transmitting the information bit sequences.The other is a full-noise channel with the capacity of 0,which only transfers the fixed bit sequences known to the receiver and the transmitter.When the code length is finite,the channel capacity is less than 1 due to the insufficient polarization of the sub-channels,which increases the error probability of decoding.Besides,the code length of the polar codes is limited by its coding structure.So it is difficult to achieve rate-compatible in practical applications.In order to solve these problems,this dissertation focus on the concatenated polar codes and the construction of rate-compatible polar codes.To improve the decoding performance,a concatenated polar codes coding scheme is designed.This scheme uses the classical block codes as the outer codes and polar codes as the inner codes.The information bits with low confidence of the sub-channel are first encoded by the outer code.Then,all information bits and the parity check bits generated by the outer code are put into the polar encoder.It is shown that allocating the most trusted sub-channels to the parity check bits generated by the outer code can improve the performance of the proposed scheme,i.e.a lower decoding error probability can be achieved.A modified successive cancellation list decoder is also proposed.This decoding algorithm chooses the one with the highest correct probability of all the checked decoding results as the final output.Simulation results show that the proposed scheme can effectively improve the performance of polar codes.Compared with the CRC-aided polar codes,this scheme has a gain of about 0.25 d B.Based on the concatenated polar code,a selective construction method for rate-compatible concatenated polar codes is also designed.Firstly,puncturing is used to generate rate-compatible concatenated polar codes.Next,weighting coefficients are selected within a prescribed range of values,and the selected weighting coefficients is used to obtain new initial parameters.Then the new initial parameters are applied to the Gaussian approximation construction method to calculate the error probability value of eachsub-channel and the reliability degree of the sub-channels is ranked according to the error probability values.Finally,the selection is performed according to the reliability ranking results.Simulation results show that the proposed method can effect the performance of concatenated polar codes under additive Gaussian white noise channel.Compared to the construction method without using the weighted coefficient,the performance of concatenated polar codes can be improved when the weighted coefficient is 0.82.