Comment on "Quasi-Cyclic Low Density Parity Check Codes From Circulant Permutation Matrices"
Comment on "Quasi-Cyclic Low Density Parity Check Codes From Circulant Permutation Matrices"
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DOI：
10.1109/tit.2008.2011508
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发表时间：
2009-03
期刊：
影响因子：
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通讯作者：
M. Hagiwara;M. Fossorier
中科院分区：
文献类型：
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作者：
M. Hagiwara;M. Fossorier
在准备[H. Hagiwara 等人，2006]，我们意识到 [M. Fossorier，2004，定理 2.3] 导致了书面上的混乱。更准确地说，只有 e1 = o2 直接从 o1 + e1 和 o2 + e2 = e 得出。另一个等式 o1 = e2 由 e1 = e2 得出，并且所考虑的两行之间的（不同的）Delta 之和必须为零。实际上，通过直接观察[M.1]中的 J = p = 2m, {Delta1,2 (I) mod p, 0 < I < L - 1} = {0,1,..., L - 1} 可以得到更简洁的证明。 Fossorier，2004，定理2.1]，使得SigmaI=0L-1 Delta1,2 (I) = m mod p ne 0。由于陈如伟最近指出了这个问题，我们决定澄清这一点。
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 = o2 directly follows from o1 + e1 and o2 + e2 = e. The other equality o1 = e2 follows from e1 = e2 and 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, 0 < I < L - 1} = {0,1,..., L - 1} from [M. Fossorier, 2004, Theorem 2.1], so that SigmaI=0L-1 Delta1,2 (I) = m mod p ne 0. Since Ruwei Chen recently pointed out this issue, we decided to clarify this point.