For practical considerations, it is essential to accelerate the convergence speed of the decoding algorithm used in an iterative decoding system. In this paper, replica versions of horizontal-shuffled decoding algorithms for low-density parity-check (LDPC) codes are proposed to improve the convergence speed of the original versions. The extrinsic information transfer (EXIT) chart technique is extended to the proposed algorithms to predict their convergence behavior. Both EXIT chart analysis and numerical results show that replica plain horizontal-shuffled (RPHS) decoding converges much faster than both plain horizontal-shuffled (PHS) decoding and the standard belief-propagation (BP) decoding. Furthermore, it is also revealed that replica group horizontal-shuffled (RGHS) decoding can increase the parallelism of RPHS decoding as well as preserve its high convergence speed if an equivalence condition is satisfied, and is thus suitable for hardware implementation.