Analytical Lower Bound on the Lifting Degree of Multiple-Edge QC-LDPC Codes With Girth 6

• Published in: IEEE communications letters Vol. 22; no. 8; pp. 1528 - 1531
• Main Authors: Sadeghi, Mohammad-Reza, Amirzade, Farzane
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-08-2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Binary system; Codes; Computer science; difference matrices; Error correcting codes; girth; Hamming distance; Hoisting; Indexes; lifting degree; Linear matrix inequalities; Low density parity check codes; Lower bounds; Matrices; Multiple-edge QC-LDPC codes; Parity check codes; protographs
• ISSN: 1089-7798; 1558-2558
• DOI: 10.1109/LCOMM.2018.2841873

Multiple-edge protographs have some advantages over single-edge protographs, such as potentially having larger minimum Hamming distance. However, most of results in the literature are related to the construction of single-edge quasi-cyclic low-density parity-check codes (QC-LDPC) codes and little research has been done for the construction of multiple-edge QC-LDPC codes. In this letter, for the first time, necessary and sufficient conditions for the exponent matrices to have multiple-edge QC-LDPC codes with girth 6 are provided. As a consequence of this letter, a lower bound on the lifting degree of regular and irregular multiple-edge QC-LDPC codes with girth 6 is derived. We also present QC-LDPC codes whose lifting degrees meet our proposed lower bound. These codes have shorter lengths compared with single-edge QC-LDPC codes. Another contribution of this letter is presenting a technique to reduce the size of the search space to find these codes.