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Recently, Low-Density Parity-Check (LDPC) codes have received much attention thanks to their near Shannon limit performance and to the ultra-efficient, high-performance Belief Propagation (BP) decoders. When compared to the prohibitively costly optimal Maximum Likelihood (ML) decoders, the sub-optimality of BP leads to performance degradation both in the waterfall region and in the error-floor region. Generally, the Frame-Error-Rate (FER) error floor of modern capacity-achieving error control codes (including LDPC codes and turbo codes) is at around 10-4 to 10-6, which is detrimental to many important applications that require very low error floor (10-12 to 10-15) such as the digital storage devices and optical communications.
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