Coding Design And Decoding Algorithm Research Of Concatenated Polar Codes

Polar Codes,proposed by Ariken in 2009,are the first new channel coding technique theoretically proven to achieve channel capacity in the Binary-Input Discrete Memoryless Channel（BI-DMC）.Because of its low coding complexity and excellent error correction performance,Polar Codes have been adopted as the standard coding scheme for 5G control channels.The coding design and decoding algorithm of concatenated Polar Codes have been the focus of research on Polar Codes,and the reliability of Polar Codes is effectively improved by the concatenating of different outer codes,so this thesis investigates the coding design and decoding algorithm of concatenated Polar Codes.First,in order to improve the reliability of concatenated Polar Codes,this thesis proposes a new coding design of Segmented Cyclic Redundancy Check（SCRC）codes concatenating Hash Polar Codes based on the scheme of Hash check codes concatenating Polar Codes,which uses segmented CRC codes and Hash check codes as the external codes.The segmented CRC codes can assist the path metric during the decoding process,while the Hash check codes checks at the end of decoding,which significantly reduces the decoding error probability and improve the decoding performance.Simulation results show that the SCRC aided Hash Polar Codes proposed in this thesis have better Block Error Rate（BLER）performance than CRC aided Hash Polar Codes.Under the Gaussian channel,when the length of the codes is 128 bit,the rate of the codes is 1/2,and the BLER is 10^-3,the new coding design proposed in this thesis gains about 0.25 dB over CRC aided Hash Polar Codes.Second,from the perspective of Systematic Polar Codes（SPC）,on the basis of the scheme for Parity Check（PC）codes concatenating CRC aided Polar Codes,this thesis proposes a systematic compiled code method of PC-CRC-concatenated Polar Codes,referred to as PC-CA-SPC concatenating codes.The concatenating design of PC codes and SPC is completed,which extends the current concatenating scheme of Polar Codes.SPC have better Bit Error Rate（BER）performance than Polar Codes,therefore,compared with the scheme for PC codes concatenating CRC aided Polar Codes,PC-CA-SPC concatenating codes with systematic coding have better performance and lower BER.The PC-CA-SPC concatenating codes proposed in this thesis gains about 0.12 dB over the scheme for PC codes concatenating CRC aided Polar Codes and about 0.35 dB over CRC aided SPC when the length of the codes is 128 bit,the rate of the codes is 1/2,and the BER is 10^-3 in a Gaussian channel.Finally,although the PC-CA-SPC concatenating codes proposed in this thesis improves the performance of finite length of the codes,the decoding algorithm of its SPC still adopts the PC aided Successive Cancellation List（PC-SCL）decoding algorithm,which has a high complexity.In this thesis,we propose the CRC aided Fast-SCL（FSCL）decoding algorithm under the SPC,referred to as USPC-CA-FSCL decoding algorithm,which uses the principle of FSCL decoding algorithm combined with the structure of SPC to reduce the decoding time complexity.The simulation results show that compared with the CRC aided SCL under the SPC decoding algorithm,the USPC-CA-FSCL decoding algorithm greatly reduces the decoding time complexity of SPC with almost no performance loss,with the N=1024,R=1/2,E_b/N₀=2d B,and L=16,the decoding time complexity is reduced by about 78%.