Reconciliation for Satellite-Based Quantum Key Distribution

This thesis reports on reconciliation schemes based on Low-Density Parity-Check (LDPC) codes in Quantum Key Distribution (QKD) protocols. It particularly focuses on a trade-off between the complexity of such reconciliation schemes and the QKD key growth, a trade-off that is critical to QKD system deployments. A key outcome of the thesis is a design of optimised schemes that maximise the QKD key growth based on finite-size keys for a range of QKD protocols. Beyond this design, the other four main contributions of the thesis are summarised as follows. First, I show that standardised short-length LDPC codes can be used for a special Discrete Variable QKD (DV-QKD) protocol and highlight the trade-off between the secret key throughput and the communication latency in space-based implementations. Second, I compare the decoding time and secret key rate performances between typical LDPC-based rate-adaptive and non-adaptive schemes for different channel conditions and show that the design of Mother codes for the rate-adaptive schemes is critical but remains an open question. Third, I demonstrate a novel design strategy that minimises the probability of the reconciliation process being the bottleneck of the overall DV-QKD system whilst achieving a target QKD rate (in bits per second) with a target ceiling on the failure probability with customised LDPC codes. Fourth, in the context of Continuous Variable QKD (CV-QKD), I construct an in-depth optimisation analysis taking both the security and the reconciliation complexity into account. The outcome of the last contribution leads to a reconciliation scheme delivering the highest secret key rate for a given processor speed which allows for the optimal solution to CV-QKD reconciliation

Multiple Parallel Concatenated Gallager Codes and Their Applications

Due to the increasing demand of high data rate of modern wireless communications, there is a significant interest in error control coding. It now plays a significant role in digital communication systems in order to overcome the weaknesses in communication channels. This thesis presents a comprehensive investigation of a class of error control codes known as Multiple Parallel Concatenated Gallager Codes (MPCGCs) obtained by the parallel concatenation of well-designed LDPC codes. MPCGCs are constructed by breaking a long and high complexity of conventional single LDPC code into three or four smaller and lower complexity LDPC codes. This design of MPCGCs is simplified as the option of selecting the component codes completely at random based on a single parameter of Mean Column Weight (MCW). MPCGCs offer flexibility and scope for improving coding performance in theoretical and practical implementation. The performance of MPCGCs is explored by evaluating these codes for both AWGN and flat Rayleigh fading channels and investigating the puncturing of these codes by a proposed novel and efficient puncturing methods for improving the coding performance. Another investigating in the deployment of MPCGCs by enhancing the performance of WiMAX system. The bit error performances are compared and the results confirm that the proposed MPCGCs-WiMAX based IEEE 802.16 standard physical layer system provides better gain compared to the single conventional LDPC-WiMAX system. The incorporation of Quasi-Cyclic QC-LDPC codes in the MPCGC structure (called QC-MPCGC) is shown to improve the overall BER performance of MPCGCs with reduced overall decoding complexity and improved flexibility by using Layered belief propagation decoding instead of the sum-product algorithm (SPA). A proposed MIMO-MPCGC structure with both a 2X2 MIMO and 2X4 MIMO configurations is developed in this thesis and shown to improve the BER performance over fading channels over the conventional LDPC structure