The Q-matrix Low-Density Parity-Check codes

Jie Xu, Zhiyong Zheng, Kun Tian

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.

Peng, LI ., Zhu +1 more

Ivan B. Djordjević

Alexey Stanyslavovych Volkov, Stanislav Sergeevich Zhuchenko

The article analyzes the famous methods of construction and representations of the check matrix block and convolutional codes with low-density parity-check. The analysis the famous methods of coding block and convolutional codes with low-density parity-check. Showed advantages and disadvantages of the known methods and allowed to identify and formulate a scientific and technical challenge. Shows the method of representation of the check matrix block codes with low-density parity-check using the Tanner graph, which like the check matrix is fully defines the parameters of the code. Check matrix of convolutional codes with low-density parity-check can also be described by Tanner graph, however, because the check matrix is infinite, then the Tanner graph is infinite. The analysis method of constructing the parity check matrix of block codes with low-density parity-check, which is based on a shortened Reed-Solomon code. Codes constructed in this method have a Tanner graph girth at least 6, which allows them to effectively use iterative decoding methods.

Dikshya Adhikari

The new developments in coding theory research have revolutionized the application of coding to practical systems. Low-Density Parity Check (LDPC) codes form a class of Shannon limit approaching codes opted for digital communication systems that require high reliability. This thesis investigates the underlying relationship between the spectral properties of the parity check matrix and LDPC decoding convergence. The bit error rate of an LDPC code is plotted for the parity check matrix that has different Second Smallest Eigenvalue Modulus (SSEM) of its corresponding Laplacian matrix. It is found that for a given (n,k) LDPC code, large SSEM has better error floor performance than low SSEM. The value of SSEM decreases as the sparseness in a parity-check matrix is increased. It was also found from the simulation that long LDPC codes have better error floor performance than short codes. This thesis outlines an approach to analyze LDPC decoding based on the eigenvalue analysis of the corresponding parity check matrix.

Ivan B. Djordjević