Research On LDPC Algorithm In Continuous Variable Quantum Communication

In the quantum communication system,the quantum secure direct communication(QSDC)realizes a real sense of the quantum communication scheme.Being different from the quantum key distribution(QKD)which needs to pre-establish a shared secret key,the QSDC can transfer the information from source to sink directly.The technology of error correction code is an important means of protecting the source against the interference,such as the environmental noise.It's an essential part of communication system.Low density parity check(LDPC)codes are the error correction code whose performance can be close to the Shannon capacity limit.In this paper,we combine the LDPC codes with the quantum detection operator to achieve hybrid error correction coding scheme.The LDPC error correction codes are used to protect the quantum state information,and the quantum detection technology is used to identify the quantum signal.The hybrid error correction mechanism can ensure the reliability and effectiveness of the communication system.A quasi quantum communication system model based on the LDPC codes is constructed,which includes the coherent state source,LDPC coded/decoded and quantum receiver.Firstly,two construction methods of LDPC codes are introduced to improve the code efficiency.One is based on the cyclic-invariant difference set(CIDS).By using the greedy algorithm,we can search the path to obtain the difference set S and then determine the check matrix.The other one is based on the protographs.By using the combinatorial designs,a systematic construction method of protographs is proposed,and then the protographs are copied T times and finally the QC LDPC codes with girth at least 12 can be obtained through permutation operation.Secondly,based on the quantum measurement hypothesis,the positive operator valued measure(POVM)is introduced to construct the quantum receiver for identifying the state of non orthogonal signal.As the quantum coherence and orthogonal properties,the received states are projected to the basis vector to construct the quantum receiver and then the quantum states are disguised by POVMs.Finally,different kinds of coherent states are taken as source to verify the quantum communication.When sending the on-off keying(OOK),binary phase shift keying(BPSK)and 4PSK signals,three kinds of quantum receivers are constructed base on the POVM operators.Meanwhile,two constructing methods of the QC LDPC codes are used to protect the signals respectively.The simulation results show that,for BER= 10-5 4PSK signal system,when the average number of noise photons N is 0.1,0.01 and 0.001,the average photon number of signal is about 22.5,15.5 and 11 respectively by using the CIDS-LDPC codes.While the average photon number of signal is about 17,11.8 and 10,respectively by using the protographs-LDPC.Therefore,we get a conclusion that the LDPC codes based on the protographs have a better coding effect and need less signal photon numbers.