Comment on "Quasi-Cyclic Low Density Parity Check Codes From Circulant Permutation Matrices"
Manabu Hagiwara, M.P.C. Fossorier · IEEE Transactions on Information Theory · 2009
While preparing [H. Hagiwara et al., 2006], we realized that the proof of [M. Fossorier, 2004, Theorem 2.3] was leading to confusion as written. More precisely, only e1= o2directly follows from o1+ e1and o2+ e2= e. The other equality o1= e2follows from e1= e2and the fact that the sum of the (distinct) Delta's between the two rows considered has to be zero. Actually, a much concise proof can be obtained by directly observing that for J = p = 2m, {Delta1,2(I) mod p, 0I=0L-1Delta1,2(I) = m mod p ne 0. Since Ruwei Chen recently pointed out this issue, we decided to clarify this point.