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Many classes of high-performance low-density parity-check (LDPC) codes are based on parity check matrices composed of permutation submatrices. We describe the design of a parallel-serial decoder architecture that can be used to map any LDPC code with such a structure to a hardware emulation platform. High-throughput emulation allows for the exploration of the low bit-error rate (BER) region and provides statistics of the error traces, which illuminate the causes of the error floors of the (2048, 1723) Reed-Solomon based LDPC (RS-LDPC) code and the (2209, 1978) array-based LDPC code. Two classes of error events are observed: oscillatory behavior and convergence to a class of non-codewords, termed absorbing sets. The influence of absorbing sets can be exacerbated by message quantization and decoder implementation. In particular, quantization and the log-tanh function approximation in sum-product decoders strongly affect which absorbing sets dominate in the errorfloor region. We show that conventional sum-product decoder implementations of the (2209, 1978) array-based LDPC code allow low-weight absorbing sets to have a strong effect, and, as a result, elevate the error floor. Dually-quantized sum-product decoders and approximate sum-product decoders alleviate the effects of low-weight absorbing sets, thereby lowering the error floor.