Low-Density Parity-Check Codes: Research Status and Development Direction

In this paper, we conclude five kinds of methods for construction of the regular low-density parity matrix H and three kinds of methods for the construction of irregular low-density parity-check matrix H. Through the analysis of the code rate and parameters of these eight kinds of structures, we find that the construction of low-density parity-check matrix tends to be more flexible and the parameter variability is enhanced. We propose that the current development cost should be lower with the progress of electronic technology and we need research on more practical Low-Density Parity-Check Codes (LDPC). Combined with the application of the quantum distribution key, we urgently need to explore the research direction of relevant theories and technologies of LDPC codes in other fields of quantum information in the future.

Design of Irregular QC-LDPC Code Based Multi-Level Coded Modulation Scheme for High Speed Optical Communication Systems

In this paper, we focus on the design of irregular QC-LDPC code based multi-level coded modulation(MLCM) scheme by jointly optimizing the component code rate and the degree distribution of the irregular QC-LDPC component code. Firstly, the sub-channel capacities of MLCM systems is analyzed and discussed, based on which the optimal component code rate can be obtained. Secondly, an extrinsic information transfer chart based two-stage searching algorithm is proposed to find the good irregular QC-LDPC code ensembles with optimal component code rates for their corresponding sub-channels. Finally, by constructing the irregular QC-LDPC component codes from the designed ensembles with the aim of possibly enlarging the girth and reducing the number of the shortest cycles, the designed irregular QC-LDPC code based 16QAM and 64QAM MLCM systems can achieve 0.4 dB and 1.2 dB net coding gain, respectively, compared with the recently proposed regular QC-LDPC code based 16QAM and 64QAM MLCM systems.

JOINT SOURCE-CHANNEL DECODING OF HUFFMAN CODES WITH LDPC CODES

In this paper, we present a Joint Source-Channel Decoding algorithm (JSCD) for Low-Density Parity Check (LDPC) codes by modifying the Sum-Product Algorithm (SPA) to account for the source redun-dancy, which results from the neighbouring Huffman coded bits. Simulations demonstrate that in the presence of source redundancy, the proposed algorithm gives better performance than the Separate Source and Channel Decoding algorithm (SSCD).

A NOVEL CONSTRUCTION OF QUANTUM LDPC CODES BASED ON CYCLIC CLASSES OF LINES IN EUCLIDEAN GEOMETRIES

The dual-containing (or self-orthogonal) formalism of Calderbank-Shor-Steane (CSS) codes provides a universal connection between a classical linear code and a Quantum Error-Correcting Code (QECC). We propose a novel class of quantum Low Density Parity Check (LDPC) codes constructed from cyclic classes of lines in Euclidean Geometry (EG). The corresponding constructed parity check matrix has quasi-cyclic structure that can be encoded flexibility, and satisfies the requirement of dual-containing quantum code. Taking the advantage of quasi-cyclic structure, we use a structured approach to construct Generalized Parity Check Matrix (GPCM). This new class of quantum codes has higher code rate, more sparse check matrix, and exactly one four-cycle in each pair of two rows. Ex-perimental results show that the proposed quantum codes, such as EG(2,q)II-QECC, EG(3,q)II-QECC, have better performance than that of other methods based on EG, over the depolarizing channel and decoded with iterative decoding based on the sum-product decoding algorithm.

Study on the Optimized Demodulation and Decoding of the BICM-ID system coded with LDPC

The demodulation and decoding solution commonly used in the bit interleaving code modulation and the LDPC coded demodulation and decoding system of the iterative decoding （BICM-ID） is to report the soft information output from the decoder of the receiver to the demodulator as priori information for completing the decoding. However, this will give rise to the reduction of the minimum Euclidean distances between codes, so that the performances of the system decline under non-fading Gaussian channel. According to this problem, an optimized iterative demodulation decoding solution is proposed and also is analyzed using simulation. The result shows that this solution can improve the demodulation and decoding performances of LDPC coded modulation and demodulation system.

Toward Efficient Quantum Key Distribution Reconciliation

In this paper, we propose how to construct a reconciliation method for the BB84 Quantum Key Distribution (QKD) protocol. Theoretically, it is unconditionally secure because it is based on the quantum laws of physics, rather than the assumed computational complexity of mathematical problems. BB84 protocol performances can be reduced by various errors and information leakages such as limited intrinsic efficiency of the protocol, imperfect devices and eavesdropping. The proposed reconciliation method allowed to weed out these errors by using Turbo codes. Since their high error correction capability implies getting low errors, this method has high performance especially when compared to the last method presented in the literature based on Low-Density Parity Check codes (LDPC). In particular, we demonstrate that our method leads to a significant improvement of the protocol security and of the Bit Error Rate (BER) even with great eavesdropping capability.

Study on the distribution law of random code structure of irregular LDPC codes and its application in eliminating short cycles

The distribution law of the random code structure of randomly constructed irregular low-density parity-check （LDPC） codes is studied, Based on the Progressive Edge-Growth （PEG） algorithm, a new algorithm which can both ellminate short cycles and keep the distribution of the random code structure is presented, The experimentsl results show that the performance of the irregular LDPC codes constructed by the new algorithm is superior to that of the PEG algorithm,

Reverse reconciliation for continuous variable quantum key distribution

An efficient and practical post-processing technique based on reverse reconciliation for continuous variable quantum key distribution is proposed and simulated with low-density parity check (LDPC) codes. MultiLevel Coding/ MultiStage Decoding, which fully utilizes optimization technique such as vector quantization and iterative decoding and the optimal channel coding most close to the Shannon limit, was used to realize efficient reverse reconciliation algorithm. Simulation results showed that the proposed method can improve the secure key distribution rate to 2.2 kb/s and the coding efficiency to 0.89 over 20 km in single-mode optical fiber. Moreover, there still is room for much improvement.