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AEU - International Journal of Electronics and Communications

Structured quasi-cyclic LDPC codes with girth 18 and column-weight

Morteza Esmaeili, Mohammad Gholami

Published Mar 21, 2009• 39 citations
Publisher
DOI
10.1016/j.aeue.2008.11.013

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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.

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In this manuscript, QC-LDPC (Quasi Cyclic Low-Density Parity Check Codes) are constructed by the diagonally Shifted Column structured Random Permutation Method (RPM) with girth 10. In this proposed method, Random Permutation based Parity Check Matrix, Base Matrix and Zero Matrices has been constructed with a column structured approach using Lower Upper decomposition technique. The row-column mapping Technique is applied to create the sparse behavior of Regular RPM based Quasi Cyclic LDPC Codes. The construction of code is obtainable by means of column weight three and row weight six. Those codes are decoded with Log Domain Sum Product Algorithm. The constructed Sparse Regular RPM-QC-LDPC Codes have low error performance and compared with other existing results.

International Journal of Engineering & Technology•Oct 14, 2018•0 citations
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.
A class of maximum-girth geometrically structured regular (n, 2, k≥5) (column-weight 2 and row-weight k) quasi-cyclic low-density parity-check (LDPC) codes is presented. The method is based on cylinder graphs and the slope concept. It is shown that the maximum girth achieved by these codes is 12. A low-complexity algorithm producing all such maximum-girth LDPC codes is given. The shortest constructed code has a length of 105. The minimum length n of a regular (2, k) LDPC code with girth g=12 determined by the Gallager bound has been achieved by the constructed codes. From the perspective of performance these codes outperform the column-weight 2 LDPC codes constructed by the previously reported methods. These codes can be encoded using an erasure decoding process.
In this manuscript, QC-LDPC (Quasi Cyclic Low-Density Parity Check Codes) are constructed by the diagonally Shifted Column structured Random Permutation Method (RPM) with girth 10. In this proposed method, Random Permutation based Parity Check Matrix, Base Matrix and Zero Matrices has been constructed with a column structured approach using Lower Upper decomposition technique. The row-column mapping Technique is applied to create the sparse behavior of Regular RPM based Quasi Cyclic LDPC Codes. The construction of code is obtainable by means of column weight three and row weight six. Those codes are decoded with Log Domain Sum Product Algorithm. The constructed Sparse Regular RPM-QC-LDPC Codes have low error performance and compared with other existing results.