Finite-length low-density parity-check (LDPC) codes under iterative message passing algorithms suffer from error floor. In this thesis, we study the harmfulness of problematic graphical structures of LDPC codes, collectively referred to as trapping sets (TSs), which play important roles in the error floor performance of LDPC codes. Our proposed methods fit in the code-independent category of techniques in estimation and analysis of TSs. The linear state-space model is a well-known code-independent method to estimate the contribution of a trapping set structure to the error floor of LDPC codes. In this thesis we first provide an in-depth analysis of this method by incorporating a more accurate model of a TS in the error floor region. We then propose an alternate code-independent technique for the error floor estimation that is applicable to any saturating iterative message-passing decoder, symmetrically quantized or unquantized, over any memoryless binary-input output-symmetric channel We also analyze and optimize the error floor of quasi-cyclic (QC) LDPC codes decoded by the sum-product algorithm (SPA) with row layered message-passing scheduling. By developing a linear model we demonstrate that the contribution of each TS to the error floor is not only a function of the topology of the TS, but also depends on the row layers in which different check nodes of the TS are located. We extend the model of row layered schedule to the column layered decoders and demonstrate that the model parameters for the latter are derived differently than those of the former. We also show that, depending on TS structures and their layer profiles, the error floor of column layered decoders can be better or worse than that of their row layered counterparts. Finally, we propose a semi-linear state-space model of TSs in which, rather than the fixed operating point of zero, used in the original linear state-space model, the operational points are estimated dynamically. Compared to the linear state-space model, the proposed method is not only more accurate, but also has the advantage of error extrapolation, i.e., error floor estimation at different signal to noise ratios (SNRs) based on the estimated error rate at a specific SNR.