QC-LDPC construction free of small size elementary trapping sets based on multiplicative subgroups of a finite field
Farzane Amirzade, Mohammad‐Reza Sadeghi, Daniel Panario · Advances in Mathematics of Communications · 2020
Trapping sets significantly influence the performance of low-density parity-check codes. An $ (a, b) $ elementary trapping set (ETS) causes high decoding failure rate and exert a strong influence on the error floor of the code, where $ a $ and $ b $ denote the size and the number of unsatisfied check-nodes in the ETS, respectively. The smallest size of an ETS in $ (3, n) $-regular LDPC codes with girth 6 is 4. In this paper, we provide sufficient conditions to construct fully connected $ (3, n) $-regular algebraic-based QC-LDPC codes with girth 6 whose Tanner graphs are free of $ (a, b) $ ETSs with $ a\leq5 $ and $ b\leq2 $. We apply these sufficient conditions to the exponent matrix of a new algebraic-based QC-LDPC code with girth at least 6. As a result, we obtain the maximum size of a submatrix of the exponent matrix which satisfies the sufficient conditions and yields a Tanner graph free of those ETSs with small size. Some algebraic-based QC-LDPC code constructions with girth 6 in the literature are special cases of our construction. Our experimental results show that removing ETSs with small size contribute to have better performance curves in the error floor region.