Study On Puncturing Polar Codes And Their Applications In Reconciliation Protocol With Delayed Error Corrction And Image Transmission

Channel codes are needed to be flexible with the respect to their code rates over time-varyingchannels. Puncturing is usually a good method to achieve the rate-compatibility. In addition, apunctured code can be constructed with arbitrary length. In this thesis, we study puncturing polarcodes and their applications in reconciliation protocol with delayed error corrction and imagetransmission system, it has an important theoretical significance.In the thesis, a novel puncturing shceme based on recovery-error probability was proposed. Inthe scheme, the punctured bits were constainted to a certain set which was corresponding to thefrozen set in order to assure that the generator matrix of punctured polar codes was a polarizationmatrix. And the effect of the channel noise on decoding was considered in choosing the puncturedpositions. The effect came from two aspects. One was the number of information bits connectionedwith code-bits by calculating the column weight of generator matrix. The other was therecovery-error probabilities to express the reliability of information-bits’ decoding results.Bhattacharryya parameter was used to evaluate the recovery-error probability of information bits.The numerical simulation results show that the puncturing scheme had a better performance thanthose with random and stopping-tree puncturing schemes. An improved random puncturing schemewas further presented where the puncturing bits were selected randomly in the certain setcorresponding to frozen set of polar codes. The simulation results showed that this scheme had abetter performacnce than those of random and stopping-tree puncturing schemes, and theperformance was improved significantly for this scheme with low puncturing rate.In additon, a reconciliation protocol for quantum-key distribution (QKD) by delayingerror-correction (EC) was proposed based on privacy amplification (PA) delaying protocol. Theproposed protocol will be useful in the secret key sharing between nodes in a QKD network wherethe nodes do not have a direct quantum link but are separately connected to a common trusted relay,and simplify the EC procedure. The security and reliability were proved on the error rate of theinformation. With polar codes, the reconciliation protocol showed that the reconciliation efficiencywas80%with code length was4096.Finally, the puncturing polar codes with the proposed schemes were applied in the delayed ECreconciliation protocol and images transmission. The simulation results showed that the proposedpuncturing schemes had a better performance than those using random and stopping-tree puncturing schemes. The results assured that the rate-compatible property were operated in imagestransmission and EC delayed reconciliation protocol.