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

作者：Sadeghi Mohammad Reza^*; Amirzade Farzane

来源：IEEE Communications Letters, 2018, 22(8): 1528-1531.

DOI：10.1109/LCOMM.2018.2841873

• Multiple-edge QC-LDPC codes
• protographs
• girth
• difference matrices
• lifting degree

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 quasicyclic 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.

• 出版日期2018-8