Research On The Encoding And Decoding Algorithm Of System Polarization Codes In 5G

The polar code is a channel coding algorithm proposed by Turkish professor Arikan,the capacity is reachable for any discrete binary memoryless channel,and the polar code is also a linear block code.Since any linear block code can be converted into a systematic code,the polar code can also be systematically encoded to obtain a systematic polar code.The systematic polar code can significantly improve bit error performance while maintaining the same low computational complexity as non-systematic polar code.In view of its superior error performance,the systematic polar code has been adopted by the fifth generation communication system?5G?as the coding mode of the control channel.In this paper the construction algorithm,coding algorithm and decoding algorithm of systematic polar code in AWGN channel are studied.The main work is as follows:1.Construction algorithm under the AWGN channel.The polarization phenomenon of the Binary Elimination Channel?BEC?is first implemented,and then two completely different construction algorithms are given based on the AWGN channel.Among them,the Bhattacharyya parameter boundary method based on Gaussian approximation is a formula for calculating the Bhattacharyya parameter from the BEC channel.The Gaussian probability density function is used to recursively calculate the exact Bhattacharyya parameter value and select the channel with a smaller Bhattacharyya parameter value,which is used to transmit information bits.The Monte Carlo-based simulation algorithm is an experimental-based statistical method.The actual bit error of each channel is obtained by a certain number of simulations,and the channel with better error performance is selected as the useful channel.Comparing and analyzing these two construction algorithms,the error performance of the Bhattacharyya parameter boundary method based on Gaussian approximation can reach 10^-4 at a low SNR and the time complexity is low.2.The encoding algorithm of the systematic polar code.Beause of the information bits in the systematic polar code are clearly visible,the coding algorithm of the systematic polar code can be roughly adopted in two ways,namely non-recursive algorithm and recursive algorithm.The non-recursive algorithm has the same low computational complexity as the non-systematic polar code encoding algorithm.The three coding algorithms used in this paper have small error performance,but the computational complexity and time complexity,the recursive coding algorithm is much more complicated and the delay is longer,so this design uses efficient non-recursive coding algorithm.3.The decoding algorithm of the systematic polar code.The non-systematic polar code decoding and re-encoding algorithm is used in decoding.The non-systematic polar code decoding algorithm obtains the estimated value of the input bit,and the information bit of the systematic code is embedded in the codeword after encoding,so it needs to be recoding again.After recoding,an estimate of the information bits is obtained.The decoding algorithm used includes successive Cancelation?SC?decoding,successive cancellation list?SCL?decoding,and CRC-assisted Successive Cancellation List decoding?CRC-SCL?.For the CRC-SCL decoding algorithm,the matching relationship between the CRC code length and the SCL decoding candidate path L is studied.