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mathematical error: swapped max lik <--> ideal observer |
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Given a received codeword <math>x \in \mathbb{F}_2^n</math>, '''ideal observer decoding''' picks a codeword <math>y \in C</math> to maximise:
:<math>\mathbb{P}(
-the codeword (or a codeword) <math>y \in C</math> that is most likely to be received as <math>x</math>.
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Given a received codeword <math>x \in \mathbb{F}_2^n</math> '''maximum likelihood decoding''' picks a codeword <math>y \in C</math> to maximise:
:<math>\mathbb{P}(
-the codeword that was most likely to have been sent given that <math>x</math> was received. Note that if all codewords are equally likely to be sent during ordinary use, then this scheme is equivalent to ''ideal observer decoding'':
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