In this letter, we analyze the convergence speed of layered decoding of block-type low-density parity-check codes and verify that the layered decoding gives faster convergence speed than the sequential decoding with randomly selected check node subsets. Also, it is shown that using more subsets than the maximum variable node degree does not improve the convergence speed.

In this paper, the cross-correlation distribution between a p-ary m-sequence s(t) and its p + 1 distinct decimated sequences s(dt + l) is derived. For an odd prime p, an even integer n, and d = pk +1 with gcd(n, k) = 1, there are p + 1 distinct decimated sequences s(dt + l), 0 ≤ l < p + 1, for a p-ary m-sequence s(t) of period pn -1 because gcd(d, pn - 1) = p + 1. The maximum magnitude of their cross-correlation values is 1 + p if l ≡ 0 mod p + 1 for n ≡ 0 mod 4 or l ≡ (p + 1)/2 mod p + 1 for n ≡ 2 mod 4 and otherwise, 1 + . Also by using s(t) and s(dt + l), a new family of p-ary sequences of period pn -1 is constructed, whose family size is pn and Cmax is 1 + p.