:<math>\mathbb{P}(x \mbox{ received} \mid y \mbox{ sent})</math>
-i.e. choose the codeword <math>y</math> that was most likely to have been sent [[conditional probability|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'':
:<math>
Line 36:
</math>
As forwith ''ideal observer decoding'', a convention must be agreed to for non-unique decoding. Again, popular such conventions are:
:# Request that the codeword be resent;
:# Choose any one of the possible decodings at random.
