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Although density evolution accurately predicts the asymptotic performance of LDPC codes, it provides limited information for codes of short or moderate block length. For this reason, combinatorial methods have been employed to analyze the performance of finite-length LDPC codes under message passing decoding. The error floor phenomenon is a key issue of finite-length effects, which is caused largely by poorly connected subgraphs residing in the LPDC codes structure. Because of the unequal noise immunity of different bit levels, error floors become more pronounced for LDPC-coded high-order modulation. Nevertheless, the enumeration of error-prone patterns that lead to error floors has been proven to be NP-hard, which motivates them to find substitute metrics with manageable complexity.
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