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Analytical Lower Bound on the Lifting Degree of Multiple-Edge QC-LDPC Codes With Girth 6 | IEEE Journals & Magazine | IEEE Xplore

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


Abstract:

Multiple-edge protographs have some advantages over single-edge protographs, such as potentially having larger minimum Hamming distance. However, most of results in the l...Show More

Abstract:

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.
Published in: IEEE Communications Letters ( Volume: 22, Issue: 8, August 2018)
Page(s): 1528 - 1531
Date of Publication: 29 May 2018

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