Reliability Measurement And Its Application In Decoding Of Polar Codes

The core of the polar code is the channel polarization theory,and it has been proved that the polar code can reach the channel capacity when the code length is infinite.However,for polar codes with short and medium code lengths,due to the insufficient channel polarization,errors occur in decoding,and the lack of decoding results detection mechanism makes the errors unable to be discovered in time,which ultimately leads to unsatisfactory decoding performance.Therefore,the decoding performance can be further improved by searching for a measure of decoding reliability,which can find decoding errors in time and take corresponding measures.The main contents of this paper include:(1)CRC is a measure of decoding reliability.In order to further improve the performance of the CRC-aided successive cancellation list(CA-SCL)algorithm,from the perspective of optimizing the CRC check,a partial CRC check-aided decoding scheme based on the critical set is proposed.CRC has changed from supervising all information bits to being only responsible for supervising the elements in the critical set,where the critical set refers to the information bits located in important positions in the polar codes.As the number of information bits for CRC supervision is reduced,the accuracy of CRC error detection in the algorithm can be improved,thereby improving the decoding performance.The simulation results show that when the bit error rate of the polar code is10^-6,the partial CRC check scheme can achieve a coding gain of about 0.5 d B compared with the global CRC check scheme.(2)CRC itself has no error correction capability,and its addition will occupy part of the reliable channel,which reduces the reliability of the channel used to transmit information bits.To solve this problem,the distance parameter is proposed and given The single-bit flipping decoding algorithm based on the distance parameter replaces the CRC in the original algorithm.In this algorithm,one bit is flipped each time and then re-decoding will obtain a decoding path,where the flipped bits are taken from the critical set.Setting the number of flips to T,and finally T+1 decoding paths can be obtained.Calculate the distance parameter value of the candidate codeword corresponding to each decoding path after re-encoding,and select the decoding path corresponding to the minimum value as the decoding result.The simulation results show that when the bit error rate of the polar code is 10^-5,the single-bit flip algorithm based on the distance parameter can achieve a coding gain about 0.2 d B compared with the single-bit flip algorithm based on CRC.(3)Both of the above two decoding reliability measures require additional calculations.In order to further reduce the complexity,this paper uses the channel polarization characteristics and proposes a new decoding reliability measure:the freezing bit difference?.This measure can be automatically obtained during the decoding process without additional calculations,and is applied to the decoding algorithm.An adaptive decoding algorithm based on?is proposed.(4)The above two decoding reliability measures require additional calculations.In order to further reduce the complexity,this paper uses the channel polarization characteristics and proposes a new decoding reliability measure:the frozen bit difference degree,This measure can be automatically obtained during the decoding process without additional calculations,and is applied to the decoding algorithm--an adaptive decoding algorithm based onis proposed.The difference degree is equal to the number of elements in the Q set whose decoding result is not 0.The Q set is composed with carefully selected frozen bits,which are selected according to the Bhattacharyya parameter or scaling exponent.The former can be quickly obtained by the simplified algorithm of the Bhattacharyya parameter.Based on,an adaptive SC-SCL decoding algorithm is proposed.After SC decoding,useto judge the reliability of the decoding result,and only trigger SCL decoding when the decoding result is unreliable.The simulation results show that when the signal-to-noise ratio is 4 d B,the SC-SCL algorithm has a 1%chance to trigger SCL decoding at most.The decoding complexity of SC-SCL algorithm is greatly reduced compared with pure SCL algorithm,but both have the same bit error rate performance.