Construction of good quasi-cyclic LDPC codes

Behzad Momahed Heravi, Sharadha Kariyawasam, Nishit Pandya +1 more

Yanhu Shan

A method to construct a flexible length or rate of quasi-cyclic Low Density Parity Check(LDPC) codes based on Balanced Incomplete Block Design(BIBD) and cycle permutation matrix is proposed.Based on actual demand,the corresponding template matrix is constructed by BIBD method.The template matrix is extended by the appropriate cycle permutation matrix.The quasi-cyclic LDPC codes constructed by the proposed method have a good structure and flexibility.This method improves the efficiency of construction good codes which meet the needs of a practical application.Simulations show that quasi-cyclic LDPC codes constructed by the proposed method perform well over AWGN channels with iterative decoding and have a lower error floor.

Farzane Amirzade, Daniel Panario, Mohammad‐Reza Sadeghi

Quantum quasi-cyclic LDPC (QQC LDPC) codes, as CSS (Calderbank, Shor, and Steane) codes, are attracting attention because of their good structure and popular channel coding schemes. Fully connected quasi-cyclic LDPC (QC-LDPC) codes with different girths which result in QQC-LDPC codes are investigated. We analytically prove that QC-LDPC codes with column weight at least 3, which yield a QQC-LDPC code, have girth at most 6. To obtain a QQC-LDPC code from QC-LDPC codes with girth more than 6 we should focus on QC-LDPC codes with column weight 2. We present an efficient and practical method to construct these codes with girth at least 8. Then, we extend our method to construct codes with column weight 2 and girth 12, thus reaching the largest possible girth.

Chao Chen

Zhou Wu-yang

A compressing method for the construction of quasi-cyclic LDPC(QC-LDPC)codes was proposed,which used a QC-LDPC code with large girth as mother code.By compressing circulant permutation matrices of the mother code,shorter QC-LDPC codes would be generated.After optimization,the generated codes would have large girth and few cycles,whose lengths varied continuously in a large range.Analysis and simulation results show that these LDPC codes have good performance and can greatly reduce the size of code storage.

Wenming Liu, Guangxi Zhu, Yongqiang Deng +1 more