QC-LDPC Codes With Large Column Weight and Free of Small Size ETSs

• Published in: IEEE communications letters Vol. 26; no. 3; pp. 500 - 504
• Main Authors: Amirzade, Farzane, Sadeghi, Mohammad-Reza, Panario, Daniel
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-03-2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: array-based LDPC codes; Binary system; Codes; Color; Computational complexity; girth; Graph coloring; Graph theory; Low density parity check codes; Mathematics; Parity check codes; QC-LDPC codes; tanner graph; Trapping; trapping sets
• ISSN: 1089-7798; 1558-2558
• DOI: 10.1109/LCOMM.2021.3138936

An approach to improve the performance of QC-LDPC codes is the removal of harmful trapping sets by increasing the girth. However, constructing these LDPC codes with large column weights and girth more than 8 is not easy. We are concerned with protograph-based LDPC codes with large column weights and free of small size trapping sets. We use the edge-coloring technique and some concepts from graph theory such as rainbow cycles to show that for large column weights the removal of all 8-cycles but the ones we call <inline-formula> <tex-math notation="LaTeX">\textit {rainbow 8-cycle} </tex-math></inline-formula> causes the elimination of several small size trapping sets. We provide a detailed theoretical analysis of these harmful trapping sets. Then, we apply them to array-based LDPC codes to significantly simplify and optimize the necessary and sufficient conditions to eliminate those 8-cycles from the Tanner graph. The given exponent matrices and simulation results show the impact of this simplification and the removal of the above mentioned 8-cycles.