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For any row weight L, several novel classes of (J = 5, L) and (J = 6, L) quasi-cyclic LDPC codes are deterministically constructed with girth eight. From these results, it is proved that (5, L) QC-LDPC codes with girth eight exist for any circulant permutation matrix (CPM) size P ≥ (2L + 3)(L - 1) + 1, and that girth-eight (6, L) QC-LDPC codes exist for any P ≥ 2(L+5)(L-1)+1. The two novel bounds...
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