Research On Degree Distribution Property And Extended Application Of LDPC Codes

Low Density Parity Check (LDPC) codes are the closest to the Shannon Limit in all of the error correction codes until now. Based on their excellent error correction performance and acceptable decoding complexity, LDPC codes are commonly used in the actual systems, especially in the optical communication systems and information storage systems. Divided from the application field of LDPC codes, the application of LDPC codes in the communication field, encryption field and quantum field is mainly researched in this thesis. By an in-depth study on the degree distribution property of LDPC codes, some improved and novel schemes are proposed in these fields. With the proposed schemes, LDPC codes can perform better than initial schemes in the above fields. The main research topics and contribution are as follows:1, The Hybrid Automatic Repeat request (HARQ) scheme based on the degree distribution of irregular LDPC codes is improved.For irregular LDPC codes, the degrees of variable nodes are not all the same, which leads to the Unequal Error Protection (UEP) property of irregular LDPC codes. Based on the UEP property of irregular LDPC codes and Signal to Noise Ratio (SNR) condition, an improved scheme about Degree Distribution Based HARQ (DDB-HARQ) scheme of LDPC codes is proposed in this dissertation. In the improved scheme, the variable nodes of irregular LDPC codes are classified into three sets, which are high degree variable nodes set, middle degree variable nodes set and low degree variable nodes set, respectively. Analyses and simulation results show that middle degree variable nodes are generally more important than the other variable nodes. The system performance of middle degree variable nodes retransmitted is better than that of the other variable nodes retransmitted.2, A Reliability Based HARQ (RB-HARQ) scheme for irregular LDPC codes is designed.Compared with normal HARQ scheme, RB-HARQ scheme can improve much system reliability and reduce some retransmission times. However, there is an important shortcoming in the RB-HARQ scheme, which is a large quantity of feedback. In order to solve this problem, a novel RB-HARQ scheme based on irregular LDPC codes is proposed in this thesis. The importance of middle degree variable nodes is also used in this scheme. During retransmission, the low reliable positions of middle degree variable nodes are returned by the receiver. Therefore, with tiny performance degradation, the proposed RB-HARQ scheme can evidently reduce much feedback overhead.3, A high order Quadrature Amplitude Modulation (QAM) scheme based on the degree distribution of irregular LDPC codes is proposed.In order to improve communication quality and promote spectral efficiency, the combination of irregular LDPC codes and high order modulation technique is analyzed. A simple and efficient combination scheme is proposed, in which the effect of degree distribution of irregular LDPC codes and the UEP property of high order QAM technique are considered. Different degree variable nodes have different protection levels during modulation mapping in the proposed scheme. It is proved that system performance is promoted using Gaussian Approximation (GA) algorithm. Simulation results also show that new scheme can reduce the system error rate.4, An early stopping scheme for the iterative carrier synchronization of LDPC codes is designed.Iterative carrier synchronization scheme based on LDPC codes can efficiently recover the carrier frequency offset and phase offset in actual systems. However, it also needs much additional computation and delay. In order to reduce some computation and delay, an early stopping scheme is proposed in this dissertation. By carefully choosing the parameters in the scheme, the number of unnecessary iteration time is reduced, and system performance is nearly as well as without early stopping scheme.5, An encryption scheme based on LDPC codes for reducing much overhead on the key size is proposed.The application of the physical layer (PHY) encryption scheme and decryption scheme is few until now. However, because the importance of information is continually increasing, it is necessary to ensure the security of each layer in the communication systems. One of the main limitations of the initial PHY encryption scheme based on the error correction codes is that the size of key is large. Therefore, at first, a permutation matrix generation scheme is proposed in order to reduce the key size. This generation scheme bases on the degree distribution property of LDPC codes and the theory on the modular arithmetic of big number. Based on this scheme and the initial PHY encryption schemes, an improved encryption scheme is proposed in this dissertation for further reducing the key size. The key of this scheme is only one big number. Analyses show that the proposed scheme can provide an acceptable security level for the communication systems. The secret key size of this scheme is much smaller than those of previous symmetric-key McEliece-like schemes. Moreover, there is no trade-off between the error correction performance and the security level in the proposed scheme.6, A kind of the trapping set of dual-containing quantum LDPC codes is researched.The quantum field is much different from the classical field, and quantum LDPC codes also have obtained much attention. In this dissertation, a special kind of the trapping set of dual-containing quantum LDPC codes is deep researched, which is named independence set for convenience. Some properties about the independence set are obtained by analyses. Moreover, based on these properties, a search algorithm is proposed in order to search small independence set. By this search algorithm, the error floor of dual-containing quantum LDPC codes can be estimated more exactly than before and better dual-containing quantum LDPC codes can be designed.