In this paper, we focus on the suboptimality of iterative decoding on graphs with cycles, through examining the use of a reliability-based decoding algorithm for some concatenated codes with an interleaver, known as turbo-like codes. The a posteriori probabilities delivered by the iterative decoding are regarded as reliability information, and an efficient algorithm for the overall linear block ... [Show full abstract] code is applied at certain iterations. Simulation results show that the suboptimality of iterative decoding due to cycles can be at least partially compensated by this approach. Some insights about the potential additional coding gains achievable are investigated based on the characteristics of the constituent decoders. These characteristics are related to the nature of suboptimality in the overall iterative decoding. The effects of some code parameters and channel conditions on the behavior of iterative decoding are also studied for a better understanding of its suboptimality.