Message-passing iterative decoders for low-density parity-check (LDPC) block codes are known to be subject to decoding failures due to so-called pseudocodewords. These failures can cause the large signal-to-noise ratio (SNR) performance of message-passing iterative decoding to be worse than that predicted by the maximum-likelihood (ML) decoding union bound.
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Smarandache et al. (2009) studied this question.
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