Parity-Check-Concatenated Polar Code And Its Construction

Polar codes have been shown to be a family of capacity-achieving codes under binary-input memoryless symmetric channels,and have been adopted as the standard coding schemes for control channels in 5G technical specification.The error performance of the polar code approaches to Shannon limit when the codeword length tends to infinity,however,it is not that impressive when the codeword length is short and moderate.In order to improve the error performance of the polar code in these cases,the parity-check-concatenated(PCC)polar code is proposed and its construction and application issues are studied in this dissertation:1)An efficient and constructible concatenation scheme with polar code,named PCC polar code,is proposed to improve the error performance of the polar codes with short and moderate codeword length.The outer and inner codes of a PCC polar code are parity-check codes and a polar code,respectively.At the receiver,the parity-check-aided successive cancellation list(SCL)decoder is adopted for the joint bit decisions between the outer and the inner code.Moreover,the minimum Hamming distance property and two simple and heuristic construction methods are provided.The simulation results show that the PCC polar codes outperform the standalone polar codes,CRC-concatenated polar codes,and the performance gain is more significant with shorter codeword length and lower code rate.2)The cluster pairwise error probability(CPEP)is proposed to analyze the elimination characteristics of the correct path in SCL decoding,and the optimization method with CPEP is proposed for the PCC polar code construction.When the list size L is limited or small,the correct path is more likely to be eliminated from the list during bit decisions,and this kind of decoding errors is named as Elimination Error in this dissertation.In order to reduce the elimination errors,the competitiveness of the correct path against the given error path is firstly measured as CPEP.Then,the CPEP is applied as the optimization criterion for the PCC polar code construction,aiming to reduce the elimination errors.The simulation results show that the PCC polar codes constructed with CPEP outperform those constructed with the random and heuristic methods.3)A repetition-concatenated(RC)polar codes as a simpler implementation of the PCC polar code is proposed to reduce the implementation,encoding and decoding complexity of the outer code in PCC polar codes.In the RC polar code,each parity bit only repeats one information bit,thus generating a repetition code,and this enables that the repetition bits could be directly assigned as their corresponding information bits without additional shift and exclusive OR(XOR)operations.In the RC polar code construction,the outer repetition codes are optimized with CPEP,which is much simpler than the optimization of parity functions in a PCC polar code.The simulation results show that the RC polar code constructed with CPEP and a small number of repetition bits could achieve nearly the same error performance of the full-check PCC polar code.4)The application of PCC polar codes in the incremental redundancy hybrid automatic repeat request(IR-HARQ)system is studied,and two construction methods based on the non-catastrophic puncturing are proposed to improve the throughput efficiency of the scheme.Considering the impact of the nested puncturing patterns on the information bit channels of the polar code,we prove that all the nested puncturing patterns in the proposed scheme would not degrade the capacities of the information bit channels into zeros,therefore the catastrophic performance loss in the IR-HARQ transmission could be avoided.The simulation results show that the proposed scheme achieves higher throughput efficiency and lower construction complexity,over the existing schemes.To conclude,in this dissertation,the PCC polar code and its construction method with CPEP are firstly proposed to improve the error performance of the polar code with short and moderate codeword length.Then,a simpler implementation of the PCC polar code,named as RC polar code,is proposed.Finally,the application of PCC polar codes in the IR-HARQ system is studied,and two construction methods based on the non-catastrophic puncturing are proposed to improve the throughput efficiency of the IR-HARQ scheme.