Slice Reconciliation Based On Polar Coding Error Correction

Quantum key distribution(QKD)is the most widely applied quantum cryptography technology.Its security is guaranteed by the fundamental theorems of quantum mechanics,such as the quantum non-cloning theorem and the uncertainty principle.It provides secret keys for the legitimate parties of secure communication.Combining one-time-pad encryption with the secret keys distributed by QKD,unconditional secure communications can be achieved.QKD protocols can be classified into discrete variable protocols and continuous variable protocols according to the modulation dimensions of the quantum states.Continuous variable quantum key distribution(CV-QKD)becomes one of the research hotspots recently because it offers the advantages of lower difficulties and costs in the preparation,transmission and detection of the quantum states.Compared with the discrete variable protocol,the post-processing of the continuous variable protocol is more complex,among which the information reconciliation is the most complicated and crucial step.Its efficiency affects both the final security key rate and transmission distance of the system.Information reconciliation consists of two parts,the reconciliation and the error correction.Slice reconciliation can achieve higher efficiency in the case of high signal to noise ratios.It converts a set of continuous variables into several sets of binary data,then corrects the errors.Thus,several error correction codes with different code rates need to be designed.In order to achieve higher reconciliation efficiency,it is necessary to apply high-performance error correction codes that approaching the Shannon limits.Researchers at home and abroad always choose low-density parity-check codes to correct the errors in the published studies.Its degree distribution is complex to design,which increases the cost of the system.Polar codes are currently the only class of codes that have been proved to achieve the Shannon limit.It has the explicit construction method that the design of the generator matrix is independent of the code rate.The encoding and decoding algorithms of polar codes can be realized recursively other than iteratively,which lowers the computational complexity.In this thesis,we proposed a slice reconciliation scheme based on polar coding error correction,and the main work of this thesis includes:1.The encoding structure and the decoding algorithms of polar codes are studied in this thesis.Frozen bits are sorted out based on the Gaussian approximation function,which increases the encoding efficiency of polar codes.The decoding algorithm is simplified by the min-sum algorithm,which reduces the computational complexity of decoding.Successive-cancellation list decoder is applied to enlarge the scope of the codewords,which promotes the decoding performance of polar codes.In this thesis we studied the slice reconciliation.The optimal interval length for different quantification levels of slice reconciliation is estimated and the corresponding quantification efficiency is calculated.The quantification efficiency over 99%is achieved at 5 levels.In the multi-level coding and multi-stage decoding procedure,the equivalent channels are modeled and the channel capacity of each level is estimated.The error correction performance is enhanced by optimizing the estimation function and the information transmission algorithm of the multi-stage decoding process.2.The slice reconciliation scheme based on polar coding error correction is proposed to reduce the design complexity of the error correcting codes at different signal to noise ratios.The computational complexity of encoding and decoding is decreased without the sacrifice of performance,which offers technical support for the practicability of the continuous-variable quantum key distribution system.The scheme is simulated and the results show that the reconciliation efficiency over 95%is obtained at the signal to noise ratios from 1 to 10.The related curve between secret key rate and transmission distance is drawn and it shows the proposed scheme can support the short distance CV-QKD system with the secret key rate from 100 kbit/s to 4.5 Mbit/s.