The maximum likelihood decoding problem can also be modeled as an integer programming problem.
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The Viterbi algorithm is the most resource-consuming, but it does the maximum likelihood decoding.
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As with other codes, the maximum likelihood decoding of an LDPC code on the binary symmetric channel is an NP-complete problem.
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The maximum likelihood decoding algorithm is an instance of the " marginalize a product function " problem which is solved by applying the generalized distributive law.
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Given a received codeword x \ in \ mathbb { F } _ 2 ^ n "'maximum likelihood decoding "'picks a codeword y \ in C that maximizes
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Note that if the probability of error on a discrete memoryless channel p is strictly less than one half, then " minimum distance decoding " is equivalent to " maximum likelihood decoding ", since if
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