Given an odd prime π and an integer π β€ π, a binary ππ Γ π 2 quasi-cyclic parity-check matrix π― (π, π) can be constructed for an array low-density parity-check (LDPC) code C (π, π). In this letter, we investigate the first separating redundancy of C (π, π). We prove that π― (π, π) is 1-separating for any pair of (π, π), from which we conclude that the first separating redundancy of C (π, π) is upper bounded by ππ. Then we show that our upper bound on the first separating redundancy of C (π, π) is tighter than the general deterministic and constructive upper bounds in the literature. For π = 2, we further prove that the first separating redundancy of C (2, π) is 2π for any odd prime π. For π β₯ 3, we conjecture that the first separating redundancy of C (π, π) is ππ for any fixed π and sufficiently large π.