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The theory of error-correcting codes stems from Shannon's 1948 _A mathematical theory of communication_, and from Hamming's 1950 "Error detecting and error correcting codes".
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Probability of false decoding with LDPC codes
It is well known that given a binary linear code $C$ under maximum likelihood decoding the probability of false decoding $P_C$ in a Binary Symmetric Channel with cross over probability $p$, in other w …